I have done two different bike excursions, but not in San Juan. One was in Mexico and it was bike 5 miles, then snorkel, then bike back. The other was in Hawaii and we bike down a big mountain, so it was easy, mostly braking and not much pedaling. The one in Mexico was more fun, but the bikes were pretty beat up. I found a specialized bike(brand name of a bike) and that was pretty good. So my advice is be careful which bike you pick and go for it. PS, It will be rather hot in San Juan in August, so be prepared for that.
Are you sure there is a bike-riding excursion in the rain forest?
The rain forest is quite a ways from the port [at least an hour, depending on traffic], and it will be hot and humid in SJ in August.
You can find info about this and other excursions at CruiseCritic.com. Click on “Boards”, then go to “Ports of Call” and either do a search or post your question there. You have to join to post a question, but it’s free.