BB does mean ball bearing.
FP is a model of OS engine discontinued before the LA series was introduced. While it is great to know someone has used this engine on the plane, the only way you'll get one is on the used engine market. Current OS offerings are LA (plain bushing, airbleed carb) and AX (ball bearings, twin needle carb).
Thunder Tiger has GP (plain bushing, airbleed carb) and PRO (ball bearings, twin needle carb).

If you want something simple, inexpensive, and new:
OS 46 LA
Thunder Tiger GP42