Local guitar & amp shops or go to Guitar Center??

If you carry it to GC they will very likely farm it out anyway. Our local GC has a guy come in one day a week to work on stuff. He's a local repairman with his own shop in town.
 
On the amp blowing fuses. Generally the Mesa stuff is built like a tank.... so a quick check at home would be to pull all the POWER TUBES out.... the biggest ones, usually either 2 or 4 of them in there. I see that BA MB uses 2 6L6 and 4 EL84 in the output stage.....  Replacing all the tubes could be a bit costly.
 
 
Get a couple of packs of fuses to experiment with. More than you will need.... maybe a dozen or so.
 
Probably the easiest and fastest way to find that bad tube is to pull the power tubes out... put a new fuse in and turn it on. The fuse should not blow. If it blows, pull ALL the tubes, install a new fuse and turn it on again. If it does blow at this point, the short is somewhere else in the amp and a service tech should look at the amp.
 
Assuming the fuse holds.... turn it off and insert the 2 6L6 tubes and turn it on.  If it holds, those tubes are good. Shut it off. Leave the 6L6's in and insert 2 of the EL84's in the sockets that are furthest apart. Turn it on again. If it holds, pull them out and insert the other 2 84's in their place. turn it on again.  At some point, the fuse should blow when the shorted tube is installed.  By trial and error, you should be able to find it quickly. Always turn it off, insert the tubes and turn it back on. Tubes can get hot very quickly so be careful not to burn yourself on the glass envelopes.
 
You can then replace the tube(s) yourself and save the shop's hourly bench fee.
 
If you have enough fuses, you can substitute the tubes with one good one and find and replace the bad one if you're in a pinch for money. If I was selling the amp, I would replace ONLY the power tube that was bad.
 
The repair shop will generally replace the bad tube only unless you instruct them to replace them all. I will probably start a war here, but, I don't see any use in replacing all the tubes in an amp "just because"..... I say replace the bad one and let it roll. It is generally not going to be a noticeable difference in the sound either way, but one way is certainly going to cost a bunch more money to do.
 
I have run tube amps for many, many years. I always kept spare fuses (lots of them) and spare tubes as well. Generally one output tube and a few preamp tubes because they do go bad. I have also run some 100w 4 tube amps with 2 tubes when one of the quads went bad and I had no spare. Tube amps are designed to handle lots of abuse so don't worry about damaging the amp with the swapping and missing tubes.
 
I have replaced all the tubes in my Mesa studio 22 (as well as other amps I have owned) and personally noticed no change in performance or tone from the old, supposedly worn out tubes to the brand new factory, high dollar matched set replacements. It is for THIS reason, I say to simply replace the bad tube and put the amp up for sale if that is your goal. I replace tubes only when they burn out the heater, short out, crack the glass envelope, become microphonic in the preamp stages, or short internally. 
 
Yes... I do agree there is a difference in tone between brands of tubes, and also from very old tubes to brand new ones. When selling the amp, that is generally not in play. The casual listener and the guy buying the amp will base their judgement and decision to buy the amp on the sound they hear when they plug in and play through it. I have never had a single person discuss the tubes in the amp when I sold the amps I have had. If that person wants, later, they can play with the tube brands to their heart's desire. If I have spare tubes for that amp that I don't need for any other amps I own, I will include the spares in the sale.
 
Anyway... try the process above and replace that bad tube if it is a tube. Save the bench fee. If you are selling the amp, repair it as inexpensively as possible. You will NOT recover the cost of new tubes all the way around in any amp you are selling.
 
Kinda like putting new, top of the line, tires on a used car before trading it in.... a waste of money.