Bridges stop working when UseBridges is set

Tor's Q&A page has a question where someone uses bridges and ExitNodes and can't get a connection. So I tried to reproduce it:

1. Retrieve some bridges (with obfs3 in this case) and enter them into torrc.
2. Set ExitNodes {US}
3. restart Tor and everything is fine.
4. Add UseBridges 1 and restart Tor.

Now Tor can't get a connection anymore. I see the following log message every second:

Apr 21 19:05:42.000 [info] should_delay_dir_fetches(): Delaying dir fetches (no running bridges known)
Apr 21 19:05:42.000 [info] compute_weighted_bandwidths(): Empty routerlist passed in to consensus weight node selection for rule weight as guard

When I remove UseBridges and restart Tor everything is fine.

While trying to tracking it down I figured out that ExitNodes doesn't play a role here. A minimal non-working torrc just needs a ClientTransportPlugin, some obfs3 bridges and UseBridges.