Bluegrass and Irish music are like walled cities. To pass inside, a secret key in needed, this being a repertoire of fiddle tunes. Unlike blues, you can't "wing it" during sessions. You must know the tunes, and learning fiddle tunes on harmonica requires some work. However, once learnt, a tune repertoire is an entry pass to sessions around the world.
Bluegrass has a basic repertoire of around 50 tunes (arguably). In my view, these are best learnt by ear, rather than by reading notation. Once learnt by ear, a tune is automatically committed to memory, and can be more easily played with others. Steve Kaufman's "4 hour Bluegrass Workout", from Homespun Tapes, is an excellent tune learning resource, featuring the basic bluegrass fiddle tune repertoire. Each tune is played at half speed, with backing, then at full speed. The melody can be turned off, leaving the backing band only. This course also teaches a good selection of fiddle tunes, see here for details.
The Irish repertoire contains far more tunes than the Bluegrass one. In particular, Irish sessions comprise sets, with 3 or more tunes, played one after the other. Hence a small repertoire is easily exhausted. Irish tunes should be learnt in sets. Once a set is under control, you can introduce it at a session, and at least be sure of what is coming next. L.E. McCullough's "121 Favorite Irish Session Tunes", also from Homespun Tapes, is a good entry to the Irish repertoire. Again, the tunes are played at half speed, with band, then at full speed.
The computer is a useful tool for learning tunes from CDs. First record the tune, and save it as a WAV aor MP3 file in your computer. Then open the file with a program like "The Amazing Slow Downer". This program allows part of a tune to be chosen, then played over and over (much simpler than rewinding cassettes). The tune can also be slowed down, while keeping the music at the same pitch. This is invaluable for learning, as many tunes are hard to decipher at full speed
Steady rhythm is a pre-requisite for playing tunes with a group. Unfortunately, this steady rhythm is best developed by playing with a group, resulting in a Catch 22. The computer can assist here. In particular, Band in a Box will turn your computer into a backing band for tune playing (and a pretty good one at that!). All you do is enter the tune chords, e.g. from the Homespun publications, set the style (e.g. bluegrass), choose the key and tempo, and the band takes over.
When learning a tune, I start with Band in a Box playing at around 2/3 of the final metronome speed. For example, I'll start with a tempo of 90 for a new Bluegrass tune, aiming for a final tempo of say 128 (a common Bluegrass speed). When I can play the tune without mistakes at 90, then I'll raise the tempo 5 clicks and repeat. Continuing in this way, the tune can eventually be brought to full speed. This is much better than fumbling a tune a full speed to begin with, as all you will do is practice your mistakes.