Bus from Playa cost around US$20 a couple of months ago. It leaves from the bus station on 20th Avenue, which runs parallel to the coast and is four blocks from 5th Avenue, the main pedestrian shopping street. NOT from the bus station near the ferry terminal, though you CAN buy your ticket there. If you can walk with your luggage, it takes maybe 20 minutes.
I prefer to have transport from Chetumal pre-organised, and I use Henry Menzies (http://belizetransfers.com/home/about
). If they know what bus you're leaving Playa on they'll meet you even if your bus is delayed. From memory he charges around US$20 or 30.
A complication is that the local taxi operators at Chetumal won't allow Belizean operators to pick people up from the bus station. Illegal - they use mob tactics. Get a local taxi to the New Market, and ask to be dropped where the buses stop. After your taxi has left your Menzies driver will appear from the shadows (!) and take you across the border.
For the trip from Corozal to San Pedro I always fly - check both Tropic and Maya websites for times and fares. My usual is the 3:30 flight, which I catch easily by leaving Playa at 9:30/9:40 that morning. I believe there is a later flight which would allow you to catch a later bus, but I've never tried it. Plane takes around 20 mins.
There is also a boat ferry service, but although it's cheaper it takes far longer and the schedule is quite restricted. Never used it.
You probably won't need to, but my journeys from Playa normally start in Europe and I stay overnight there. My preference is Hotel Casa de las Flores, about midway between the two bus stations on 20th.