I have had quite a bit of experience with this. Firstly the music itself must be designed in a way as such the passages under the dialogue need to be much more underscore orientated rather than melodic. You give no information as to what the music actually is and where it comes from.
As a TV and film composer myself it is important to not get too busy or melodic under any dialogue. eg a soprano sax solo under a dialog passage is out. Get what I mean.
Many composers fail in this regard by the way.
Dont let the dialogue get buried either. Sometimes it annoys me a lot when the mixers are pushing the music so hard you cannot actually hear the dialogue. Your director should keep you on the straight and narrow with this.
If you have no control over the music
(ie production library music) then there are other things you can do. One is insert a dip in the frequency response of the music as well around the mid and upper mid range frequencies when the dialogue is present. ie make room for the dialogue like we do with carving a little hole in the response of instruments for vocals in a music mix etc.. A dynamic equaliser is handy here and you could also side chain this to the dialogue track too. Note the music should come back to normal response wise when the dialogue is not present and smoothly as well. ie you should not notice the change in the music EQ either.
But from what I can see and having sat in a lot of audio dubs, automation is still the main key here. Ducking can sound a little too obvious if done poorly and is not the way really. If you are good with the automation you can lift and lower music levels so subtly that you should not really even hear or notice the changes.
The final sound mix for any TV production usually takes around a 10:1 ratio. ie it takes 10 hours to mix a 1 hour production usually. There is no fast way here. Especially if SFX are involved as well both Foley and atmos related.