Ah yeah, I didnt thikn about the bees needing a view of the sky...hmmm could create a giant skylight for them or just have bees above ground and nothing else. Thanks!
Like Matpower123 mentioned, you can breed the bees to work under ground. The trait is called 'cave dwelling', and can be easily gotten from the rocky / stony bees, or mutated in with serums if you use the extra bees-stuff.
On the occasions where I've done underground-basey-stuff, I've always used initial skylights over things needing sunlight, and then covered them up as I become able to alleviate the need. Outside, who needs it!
The biggest problem would be space, how would you create it? In my case I had a mining laser set to explosive which allowed me to go to town on the inside of my mountain base. If you don't have access to that tool, you may have to get a bit creative. TNT, etc. is another choice, but how are you going to obtain all that gun powder. Mining it out by hand is an arduous task. Consider the amount of time it would take to clear out a space, even a 20x20 space (400 blocks). If you consider that it takes 1-2s per block that's 400-800s or 6-12 or so minutes. Ever expansion to your base's space needs would require this much time.
A buildcraft filler or quarry can work wonders when it comes to clearing out underground space. If you use a filler to clear room-like shapes, the power consumption isn't all that overwhelming since you'll only be running it for a short period of time.
Tinker's construct hammers (even ones made of really bad materials) can clear rooms right the heck out in no time.
Manual mining with vanilla tools is time consuming, but depending on your playstyle perfectly viable. I've often cleared large spaces while watching a movie or youtube stuff or something. It's nice for times when you don't feel like thinking too much.
. I prevent mistakes by laying out the area first, placing torches or some other marker where I need to stop digging.