Welcome to the forum!
My wife and I fished Ascension Bay about 2 years ago. We stay in the Sian Ka'an Biosphere (on the Boca Paila) in a place called Pesca Maya.
Chances of renting a car are pretty good in the Tulum area. Your hotel can probably arrange that for you.
As far as fishing goes; for Bonefish and Permit, the best fishing is not in the Boca Paila itself, but more like 20 miles across Ascension Bay on the flats. You can defintely hook some Bones on the BP and, of course, there are always Jacks in the surf. But for quantity, you really need to get to the flats.
You can check with outfits like Yellow Dog, Boca Paila and Pesca Maya. I think that all of them offer day trips to the flats. It starts early, but you'll need 2+ hours to get from your hotel to the flats. They pick you up at your hotel, feed you and get you to the good spots.
You may be able to make contact with someone in Punta Allen; the last stop on the Boca Paila and they may be willing to take you out to the flats for less than what the others like YD, BP and PM charge. But, you usually get what you pay for. So, you may want to consider a splurge and go with one of the groups that makes a living doing this. Or, as you said, you can always fish from the surf and there are some very nice beaches as you go down the BP; even before you get to the Sian Ka'an Biosphere (Sian Ka'an charges an entry fee, but it's nominal).
Good luck / have fun!