Do the buses pick people up for CBR at the TTC?
There are ONLY 2 Disney Transport buses at the TTC. One goes between the TTC and Animal Kingdom, and the other goes between the TTC and Disney's Hollywood Studios.
There is no such thing as a bus between the TTC and a Disney owned-and-operated resort, such as Caribbean Beach Resort.
I remember during our first trip, when we stayed at CBR coincidentally, my 5 year old son was disappointed that we never rode the monorail. So after leaving the Magic KIngdom on our last night, my wife took our 2 year old daughter back to CBR by bus, and my son and I went to the monoail station to ride the loop around Seven Seas Lagoon. We got off the monorail at the same place we got on, Magic Kingdom, and then walked to the bus area and took the bus back to CBR.
There are 3 monorail lines: resort, express, and Epcot.
The resort and express monorails run paralell to each other. Both of them make a complete loop around Seven Seas Lagoon. The resort monorail runs clockwise and stops at Magic Kingdom, then Contemporary Resort, then the TTC, then Polynesian Resort, then Grand Floridian, then back to MK, and so on. The express monorail stops ONLY at the TTC and MK. It runs counter-clockwise. It chugs right past Grand Floridian and Polynesian, and chugs right THROUGH Contemporary, but doesn't stop at any of those resorts.
The Epcot beam has only 2 stops, the TTC and Epcot.
If you have time to kill one morning, you could take the bus from CBR to Epcot, then hop on the monorail from Epcot to TTC. AT the TTC, you'd need to get off that monorail train, and either go up to a different monorail platform to catch the express or resort monorail to MK (the express weill be much faster), OR you could take the ferry from the TTC to MK. Doing this will take an unnecessarily long time as compared with just taking the bus from CBR to MK, but it will give you a lot of monorail time.