And here's a simple answer
What time does your flight arrive at BZ International? How many in your party? How much luggage do you have?
I ask because if your flight arrives later in the day, it it a timing issue. Just take a Tropic Air or Maya Air flight out of BZ International direct to San Pedro. If you get in earlier in the day and don't have a bunch of luggage you can take the water taxi from BZ City to San Pedro.
If there are a bunch of you in your party and you get in earlier in the day, you can grab a taxi over to the Municipal Airport (about $20) and fly to SP from there. Will save you money if you are four or more bodies in your party, not really worth it for two or less, IMO.
Me, I'd rather just pay the bit extra for the flight from BZ Int. and have my feet up with my first Beliken ASAP.