This as Kylotan has also noticed: 
Example... Tonight I recorded a clean bass track, cloned that track and added EQ and a little dirt to it. Somehow some of the drum track bled into that making some of the cymbals sound harsh.
 
This should not happen in a normal setting. 
This could only happen by the playback looping into a newly recorded track somehow. 
There's no way one audio track "bleeds" into another ever on a DAW.. On tape yes. 
 
And often 3rd party vst's that no one else has used can be in question as to what they do behind your back. Try using Sonars tools first. 
 
Be aware that using "clone" has it's pitfalls. All editing is shared between the 2 tracks thereafter. 
It's best to copy/ paste into a new audio track if you wish to edit only one of the tracks.
 
And 2 bass tracks to me is a no no. Use one track as the source and send it to 2 different busses where you can experiment with effects would be smarter. 
 
If good bass tone is important to you, start with upgrading the Pick ups and new strings for the bass. 
Often a good bass tone can be achived with the right instrument. 
I use a Joe Meek 3 Q to record bass , it made a huge differance so consider purchasing a good pre amp as a upgrade to your recording gear.  
 

I think that vid was was Glenn Fricker, not Ola.
 
Another way of doing it:
 - Clone the clean bass track and add the distorto fx to the second track.
 - Low pass the clean track somewhere around 300Hz
 - High pass the distorto track around the same 300Hz
 - Adjust the "crossover" clean/dirty to taste - might be 250Hz, might be 400Hz.
 - Blend the two tracks to get a good composite sound.
 - Send output to a bus and comp/eq as needed.
 - Maybe comp/eq the clean/low, distorted/high tracks if necessary.     
 
This will keep the low thump more defined so it doesn't mush out with the distorto.  

Thanks guys. I'll give it another go tonight and experiment with it. Once again, some good info, much appreciated. :)
 

Jeff M.
I think that vid was was Glenn Fricker, not Ola.
 
Another way of doing it:
 - Clone the clean bass track and add the distorto fx to the second track.
 - Low pass the clean track somewhere around 300Hz
 - High pass the distorto track around the same 300Hz
 - Adjust the "crossover" clean/dirty to taste - might be 250Hz, might be 400Hz.
 - Blend the two tracks to get a good composite sound.
 - Send output to a bus and comp/eq as needed.
 - Maybe comp/eq the clean/low, distorted/high tracks if necessary.     
 
This will keep the low thump more defined so it doesn't mush out with the distorto.  

You are correct, Glenn does have a video that I watched as well. Glenn basically says the same thing Ola does. After watching it again I realized I did some stuff wrong. I'll give what you said a go too.
 
Thanks again, guys. :)

With the above mentioned plugins, I tried again. Did everything as instructed. When the original tracked was cloned I noticed I couldn't solo the cloned until I turned off the EQ. Then the same thing happened to the original ultimately resulting in muted playback on both tracks until that EQ was turned off.
 
Seems a bit strange to me. Is there a reason it would do that?

Cactus Music
 
Be aware that using "clone" has it's pitfalls. All editing is shared between the 2 tracks thereafter. 
It's best to copy/ paste into a new audio track if you wish to edit only one of the tracks.
 

 
I am not sure that this is true.  There are problems with S.I. tracks, where both tracks use the same synth, but I am pretty sure that a cloned audio track is entirely separate from the original.
 
OP - As for bleed on the bass track, I think it is likely that your bass pick-ups are microphonic.  Try recording the tack whilst monitoring over headphones.

jb101

Cactus Music
 
Be aware that using "clone" has it's pitfalls. All editing is shared between the 2 tracks thereafter. 
It's best to copy/ paste into a new audio track if you wish to edit only one of the tracks.
 

 
I am not sure that this is true.  There are problems with S.I. tracks, where both tracks use the same synth, but I am pretty sure that a cloned audio track is entirely separate from the original.
 
OP - As for bleed on the bass track, I think it is likely that your bass pick-ups are microphonic.  Try recording the tack whilst monitoring over headphones.

Actually, I do all of my recording that way. I don't have a bass amp, so it's all straight in.
 
Even though I got the results I wanted by simply using a different EQ, I'm not sure that it is that particular EQ causing the problem.
 
Oh and I forgot to mention that I did try copy/paste into a new track and the same thing happened.

Hi. Is this something that occurred before you installed Equilibre?  If it is behaving differently with another EQ, I would say that your Equilibre EQ might be to blame in this case.
Are there any updates to that plugin, that you have not installed yet?
Best of luck.

My $02:
 
- I think I can safely say that one track's audio being affected by FX in the bin of another track via signal paths within SONAR is not going to happen unless there is something seriously corrupted (and never previously reported to my knowledge) in a particular project.
 
- Cloning Audio tracks with FX should not create any linkage; I seem to recall there was an issue with this at one point, but I believe it was resolved quite some time ago.
 
- That said, cloning the track should not be necessary; it's just doubling the amplitude of the raw recording, which will make it louder but not "fatter". If you can't get the effect you want using insert FX in the bin of the one track (e.g. parallel compression), a send to a bus should be used to get the parallel path instead of cloning the track.

Cloning DI bass is indeed a common technique. I haven't seen those specific vids but have seen/read similar tuts detailing that process. You keep the original, clone twice, on one of the clones you add the dirt (with a sim or simple tube saturation) on another you dial in the pick sound (and roll off the lows). The original is the clean meat sound. You can roll off the tops and dial in the bottom end better because the other two tracks are taking care of the definition and tone. There are other ways to screw around with this stuff as well with two tracks or messing with what does what. It's kind of neat but I've moved on to other ways to get the bass sound I like.
 
They are not exact clones because you alter the sound of each track significantly so it doesn't just "sum" as one and merely add volume. It's a blending trick. It's almost like splitting out the freqs of a guitar signal with a multiband compressor (set to NOT compress... just silence all but one band) and clones then dialing in each range individually with whatever effects you are using.
 
Not saying it's the greatest technique but I've used it extensively in the past and it can do some interesting stuff. Kind of a PITA actually and can get muddy real quick in a thick mix though which is why I've kind of stepped back from it.
 
That has nothing to do with whatever weirdness OP was describing but I saw some people saying that cloning bass in this manner was not legit. Try it out.

Personally I don't bother cloning any tracks. I create a bus for the 'grit' aspect of the bass, where I apply saturation/distortion/amp simulation and maybe a high pass afterwards if needed, then that is routed to another bus which sums the original bass track plus the grit bus.
 
But none of that explains what is going wrong here. I can think of no reason at all why Sonar would not let you solo a track based on the state of some plugin, and I don't think I have ever encountered anything like that. I'd love to see what you were doing because something very weird is happening.