The airlines are now requesting passengers to check-in 3 hours before departure time, which means 7am for a 10am flight, so I'd stay close to the airport.
To answer your questions, the trip from Placencia to Belize City is about 3.5 to 4 hours by car, and a bit longer by bus (4 to 4.5 hours). With a group, the best idea might be to hire a private transfer service and split the cost. Also check the websites of the two airlines, Tropic Air and Maya Island Air, if you want to look at flying from Placencia to BC.
Ritchie's Bus Service runs buses to/from Placencia, but none directly to BC in the afternoon -- you'll have to go to Dangriga, then Belmopan then BC making changes at some or all of those places.
http://www.ritchiesbusservice.com/schedules--connections.html
James Bus Line runs buses from Independence to BC. Check the schedule here...
https://www.hickatee.com/belize_bus_times.html
You can get to Independence on the Hokey Pokey water taxi/ferry.
All buses terminate at the bus terminal in BC.
Taxi fare from BC to International airport is BZ$50 (or US$25) per taxi.
For a cheap way to get back to the airport from Belize City, get a bus to the airport turnoff in Ladyville, and either walk the 2.5 km to the terminal, or look around for a taxi. Bus fare from Belize City is BZ$1 or $2, and the taxi probably won’t be more than BZ$10.