Given the conditions, I'd say give it a try. You'll probably hurt afterward because the bike riding will be different from the exercise you're getting now. Riding a bike 45 miles is about the same in energy requirement as running 5 miles or so unless you're riding faster than around 12 miles per hour.
You have places to stop, not many hills, plenty of time, and friends to come and get you if it turns out things don't go well. Make sure the bike is in good shape first.