Hi Kim-
I too am an avid road cyclist. I'm almost 4 mos. post-op from my bilateral performed by Dr. Su. I started stationary bike right after my one month checkup as part of my 3 days-a-week PT (at a sports rehab facility, supervised by therapists) sessions. I did about 10-15 mins on the bike each session followed by strengthening (fitness ball squats against a wall, step-ups on an 12 in. platform, single-leg raises) and then stretching (hamstring, quad, hip flexors). I progressed to add in other hip exercises using a 'hip machine' during the 6 weeks of organized PT. At this point I'm back to doing 2-3 mile hikes (with my trusted Golden Retriever, Sully) and I'm back to spin classes (taking it easy, low resistance, and staying mainly in seated position). I make sure that I always follow up spinning with the recommended stretches. Post-spinning, the hips are really feeling pretty darn good. I'm not having any pain while spinning.
I'm planning on getting back on my road bike this weekend, but I'll do flat rides in a low gear. Of course, falls are a concern, so I'll be very conscious of taking it easy.
So, I'd say to wait at least until you've gotten past the groin pain and have your 'cycling strength' back before you venture out on the roads.
Hope this helps....good luck.