So I'm currently in two bands. One of which has been on the rise quite quickly recently. Within several months we've gone from being completely unknown to being offered several shows, being friends with several of the top bands in our local scene as well as several promoters. We obviously aren't content with where we are but are pleased with the progress. My second band is less so; we've played more shows, but aren't as popular. It's a far less active band, but since it's essentially a side project for me that's ok.

However, recently, a guy in one of the top bands in our scene has asked me to fill in the second guitar position in his band. These guys are real busy as a band, they play gigs almost regularly, play regional shows, and open for some big bands when they come through. He and I have already agreed that I won't leave my other bands (and TBH had he said I had to I would have flat out told him no), and I feel like that this is a great opportunity for me. Great dudes, good music, good shows, and I wouldn't have to worry so much on the creative side because I can trust them to write the good stuff.

However, I don't really know how exactly to bring this up to my other bandmates. I'm not sure how they'll take me being in another band, especially this one. I don't feel like it'll harm my main band much, I'll still be fully dedicated to it (it's my baby), and it won't really affect that band's shows outside of me possibly pulling double duty a decent bit. How exactly do I do so?
Well, here's the thing.

You need to decide, and then communicate to members of all three bands, what your priorities are and what you will do when those priorities come into conflict.

The most important of these is gigging. What will you do if a gig from one band comes up that gets in the way of a gig from the other band? You have to decide this now and communicate it to members of both bands.

Rehearsal is less crucial, because you should be able to schedule rehearsal around your other band's requirements the same way you schedule it around other jobs/school/whatever.

But you essentially have to negotiate with two of these bands how you'll handle conflicts, but real and potential, and come to an agreement that is okay with the bands you're placing a lower priority on which they won't be resentful of. Sounds like the older band is your lowest priority, but the other two are something you're going to have to figure out.

ps congrats on the success, sounds like things are going great for you!
Yeah, that is the major problem. Typically I go on a first come, first serve basis; whoever books a date first is the first band I'll play a show with. Shows within this little group rarely overlap, very rarely will you see two bands in this community playing two separate shows on the same night, if it's the same night it's typically the same show. Not that I'm saying this won't ever be a problem. but not too terribly much.

Of course you're right, and setting priorities between this new band and my main one will be the big deal. Obviously, like you said, my side-project will be on the bottom of the list. Essentially my goal is to keep them equal for me, and again, the fact that I won't have to necessarily write music for the new group will help greatly. Their old second guitarist is in a similar boat to me, and he's managed to balance his bands well.
Well, if this band is going pretty good you should take it, any way to gain local notice as the guitarist of 3 semi-regularly gigging bands could help you get a career in music. If there are no schedule conflicts, what could possibly go wrong?