It depends on the geo-graphical setup of the bridges..
You do need one bridge as "Root" alteast but traffic from one non-root to other non-root dosen't always have to go through the root..You can have non-root bridges associated with non-root as well but one of the non-root in that chain needs to have associated with root which is must..Like following
NR1-----NR2-----NR3----NR4-----Root
(you can have root anywhere in that chain)
So if root is not there, all the non-roots (NR1-4) will loos the association..So here traffic from NR1 to NR3 will go through NR2 but not through Root..