I'm not sure why all you could find were combo tours. If you google "La Paz Waterfall Costa Rica", the La Paz website itself comes out on top. Their prices are the same as the rack rates that were quoted on the Viatur link that Nebru provided but, like Viejo suggested, the La Paz website provides much more information and I'd add that it is usually preferable to deal direct with a place than to go through a middleman even if the price is the same. BTW, that link is
http://www.waterfallgardens.com/lapaz-waterfallgardenspark.html.
I'd also add a couple of more thoughts. If you have a rental car to get there anyway or plan to stay overnight there (Zippy is right that the rooms are nice as well they should be STARTING at $235/nt this time of year), then, great, go their yourself and just pay the basic entry rate rather than go with a tour pickup in SJ. Otherwise, I wouldn't be so sure there will be much to gain by doing it independently. The basic entry to the park without anything else is already $32. That does not include their buffet lunch which comes to $44 along with park entrance. The tour package which includes pick and drop-off from the front door of your hotel in SJ, park entrance, lunch buffet AND a personal guide for your group who will walk you through the whole place is $65. That's just $21-33 more than the other packages, so why pay $50 for private round trip transportation from SJ? I'm not sure what Alex would charge but I'd bet it is more than $21. Okay, maybe it would pay if you had someone else to split the taxi fee with.
Aside from that, the added flexibility of a private driver does not really mean that much for an activity such as this. With their tour, pickup time is between 10-11AM (ie not too early even for those who have been up all night at the HDR/BM) with return between 3-4PM (ie early enough to get in a quick MP session and still make it to CRT happy hour). You might want to get there earlier to try and beat the crowds, but you're probably going to want to spend a few hours there and most likely will be there during the middle part of the day like everyone else. And while they don't close until 5PM, you'll probably be ready to return to SJ by the time the shuttle van leaves. What I think the biggest advantage of a private driver is not so much the flexibility of choosing your departure times as it is not having to waste all that time driving around to all the various hotels to pick-up your fellow tour participants (including waiting for that hungover monger that overslept).
As for public bus, I think you can really completely forget about that for this destination. Yes there are public buses to Irazu and Poas, but I wouldn't call just 1 bus there and another one back each day a wealth of options. And those are national public parks that get many tico visitors. I doubt that many gringos use the public buses to get to either of those places. La Paz is a privately owned park and the base admission price is well out of the reach of most ticos (so much much fewer of them go there). Again, I doubt many of their gringo customers would even consider taking a bus to get there, even if there were one to take. BTW, if there is a bus it would probably be one between Alajuela (ie involving a transfer there) and Puerto Viejo de Sarapiqui by way of San Miguel (ie meaning jumping off the bus somewhere after Varablanca), but I haven't been able to find anything suggesting such a bus route exists.
That said, here are links to on-line bus schedules in general. I don't know how up to date they are but in my experience the schedules really don't change that much (except for prices that have been going up due to rising fuel costs). The first one is from the ICT website (how much more authoritative can you get than that):
http://www.visitcostarica.com/ict/paginas/LEYES/pdf/ItinerarioBuses_en.pdf. The other one is from a private website, so perhaps not so official, but has a search interface that makes it easier to use and get complete info (not just between SJ and other places but also between various points in CR):
http://costa-rica-guide.com/travel/index.php?option=com_content&task=view&id=454&Itemid=684