I would do this:
sudo strace -pXXXX -tfo /tmp/strace.log
where XXXX is the process id of bash. In a quick check of filename completion on one of my NFS-mounted directory trees, it works without problems:
-f
Trace child processes as they are created by currently traced processes as a result of the fork(2) system call.
-t
Prefix each line of the trace with the time of day.
Some people might prefer -r:
-r
Print a relative timestamp upon entry to each system call. This records the time difference between the beginning of successive system calls.