Congrats on your (soon-to-be) new boat!
As an avid cyclist myself, I have had to deal with this issue too. Without a much larger boat, there does not seem to be a perfect solution to bike storage. But there are some imperfect ways to get by.
I sometimes bring my bike with me on Chesapeake cruises, especially if I know we'll be staying put for a few days in one spot on the Eastern Shore (an ideal destination for cycling, incidentally -- that is, if you don't mind riding on flat.)
How do I transport the bike? Well, we have mast pulpits on our boat. Since our boat is set up with all lines led aft to the cockpit, the mast pulpits really double nicely as bike racks. If we didn't have mast pulpits, I would probably rig some way to stow the bike off the stern pulpit.
But you don't necessarily have to bring the bike aboard to integrate cycling into your sailing schedule.
Sometimes, I just bring the bike along on the car's rack, and go for a ride while still at our marina. If you plan to do a lot of 3-day weekends on the boat, this might be a nice way to decompress before and after your 2.5 hour drive. It would be a good opportunity to ride in a new venue, with the benefit of returning to a shower at the marina.
But, ultimately, you shouldn't worry about it too much if you take a couple days off from riding while you sail around -- it's actually good for your body and riding strength to take an occasional 2-3+ day rest. You'll likely bounce back even stronger. Plus you get to focus on the sailing -- which is good for you too.
P.S. As for the suggestions about renting... I got the impression gbm was asking about fitness riding, not just poking around a town or port. Rental bikes would be fine for poking around. But when we're talking about going out on a 20-40 mile ride, fitness riders usually want to ride their own bike or something comparable. Most rental and folding bikes I've seen would be disappointing in that respect.
However, Bike Friday makes some serious
folding bikes if that seems like a good option for you.