You’re right, Alajuela is closer to the airport than San Jose and you can get a shuttle from there right to the dock that goes to Tortuguero. The shuttle companies usually don’t do pickups from hotels in Alajuela though so you have to get to a designated pickup location. You can either go to the closest hotel or the generic pickup spot for the company. For Caribe Shuttle, one of the companies that goes that route, it’s Denny’s restaurant near the airport. Cab fare will be around $10 depending on where you’re staying in Alajuela.
For the bus, you would definitely have to get to San Jose. Buses for Carairi leave from the Gran Caribe terminal in downtown. It can be a long, sometimes pricey cab ride from Alajuela to San Jose depending on where you’re staying and traffic, so make sure to take that into consideration. Flying is also an option- Nature Air and Sansa both offer daily flights starting at $59 that are less than an hour. Hope that helps. Let us know if you have any more questions.