15 urban miles each way is certainly doable, but it's a significant commitment. My 9.5 mile each way suburban/urban commute, with decent cycling infrastructure, is about 45 minutes (with mostly good attention paid to the rules of the road, I'm not jumping red lights and such). 15 miles is at least an hour each way unless you're on wide open roads the whole time, potentially more.
That said, it sounds like your other option is public transportation that is probably taking you at least as much time? In that case, getting some exercise, maybe saving some time, and definitely saving money makes this a potentially good proposition.
I'd recommend trying it out one day, maybe on a weekend, to check out the route, make sure you know how to get there, there aren't any crazy dangerous things, etc. If it seems doable, go for it. No need to spend much on a bike to start with, just get something that goes and is reasonably comfortable and give it a shot. Even better if you could borrow a bike just to try it.