There are shared shuttles (vans), hotel to hotel, Interbus or Zuma Tours, approximate travel time from San José to MP is 4 hrs, Interbus is $64 pp one way (estimated: 8 am - 2 pm). See the Transport Planner: https://geckotrail.com/transportation/ .
This blog has suggestions on directions from SJ: https:/… .
Your fastest option is Sansa. There are 6 flights each day from San Jose (SJO) to Tambor and 6-7 flights from Tambor back to SJO. Price varies from $90-93 US for Promo seats and $114 if you miss the Promo deals.
The sooner you book your flight, the cheaper it is.
As Seaturtlewoman suggested, car rental is available near the airstrip (Budget) and cabs and shuttles wait for arriving flights for other transport options.
Happylittlefish, can you please share the shuttle bus company name and what time the shuttle picked you up at the airport? There are many shuttle buses and all have different pick up times from various locations. I was not aware of an airport pick up as most of the shuttles have pick up stops at hotels and B & Bs.