You can bid for what you like! What you get will be dictated by the seniority system. If you insist on remaining on the top fleet, expect to wait, and possibly having a tough time on the command course. You can move off on to less popular fleets and have an earlier command. You can move off earlier and get well practised so a simple move to the left seat is simple.
I believe a regualr change is good for you. i always felt after about 6 years on a plane, you got technically stale. A transfer was always very good, a mental 'kick up the backside'. The trouble was, you didn't know what you had forgotten. The best guys technically were the ones fresh on the fleet. After years of getting fat, dumb and happy flying the best routes on the best aeroplanes and struggling to do 1 landing in 28 days, trying to move seat, type and route structure altogether was, for several I knew, a step too far.