Actually, the typical index can be rebuilt online. You do this by specifying "alter index index_name rebuild online". The old index structure continues to be available to other users during the rebuild.
It's true that bitmap indexes don't support online rebuilds. However, the entire database need not be offline to do the rebuild. Oracle will acquire the necessary locks, and other users will have to wait while the rebuild finishes. As a result, bitmap index rebuilds should typically be done in off-peak hours to minimize contention.