One bloom filter advertised by and received from each peer is kept locally.
Whenever an update comes from a peer, if it is different from what is already stored, the node will update its local copy, then:
For each remaining peer that is either a spanning tree parent or child, calculate a new bloom filter consisting of the union (XOR) of all the other peers and send it.
This is called "split horizon" routing and essentially means that after convergence each node has a bloom filter for each of its peers containing all nodes reachable through that peer.
Later, at the routing stage, the node can examine all its peers' bloom filters to identify candidate next hops for routing.