I'll be moving to BA on the 777 soon. The rosters are definately not 6 on 6 off. Expect 4-5 trips a month with no set pattern.
Initially you will be on 'blindline' where you are basically given a roster although you can state preferences. Once you have some seniority you then bid for lines of work.
Looking at a bidpack for oct05 a typical month:
5-7th: JFK
12-15th: ORD
18-20th: PHL
23-26th: MCO
29-31: DEN
777 apparantly not as commuter friendly as 747.