Law enforcement would need to work with ISPs in order to determine if one of their clients is using Tor. However the infrastructure for this is already completely in place as mandated by CALEA. Law enforcement will never need a warrant to determine if someone who is not using a bridge is using Tor, trap and trace has no requirement for a warrant as it looks at who the target communicates with rather than what they say. If the target communicates with a known Tor relay, it is quite trivial to determine that the target uses the Tor network without the need for a warrant. Using bridges helps to protect from this though. It is not likely that LE will order trap and traces on thousands of people to narrow in on one target, but it is entirely within the realm of possibility that they will confirm that Alice uses Tor after determining that she is a likely suspect.