I'm starting to learn finger style guitar and I have no idea how I should include a bass rhythm with the lead bits I play. Any suggested practice techniques? anything I should try doing other than breaking apart the different rhythms of each and practicing them individually?
Don't break apart the different rhythms and practice them individually. At this stage, it's more effective if you don't think of yourself playing two separate parts simultaneously. Instead, think of playing one part that happens to have two or more notes at a time and start slowly.
For example, here's a typical Travis-picking bass-and-lead bit on a C chord:
$A.3.$B.1 $D 2 $G 0 $A 3 $B 1 $D 2 $G 0
In this bit, the bass part alternates between the A string and the D string, while the melody alternates between the B and G string. But rather than thinking of this as separate bass and melody parts, you should think "On the first beat, play both the A and B strings. On the second beat, just play the D string followed by the G string, etc."
What you're doing is training your fingers and muscles to physically play the notes. As you get better and more comfortable with that, your brain will stop having to focus so intently on getting your fingers to behave and can focus more on making it sound like two independent parts.
I once saw a drumming DVD with Steve Smith (the drummer in Journey and other bands) in which he talked about developing independence between his limbs. He talked about how, when he wants to learn a new rhythm, he writes out all the parts on a single staff and then, painfully slowly, practices it as if it's one rhythm with multiple notes rather than four different things going on at once. So he'll be like, "Okay, on beat one, I play the bass drum and the ride. On beat two I play the snare, the hi hat, and the crash" or whatever.
If you think about it, you're doing much the same thing. This same idea is how you want to start building up your ability to play multiple lines simultaneously.