The BEDFORD group in 1901 does indeed look promising.
The person you've identified as Rich is female (see the column in which her name appears) and "married", and I think the name actually says "Riah".
So is this Maria, in disguise, with her new man Tom Bedford, pretending to be his wife?
Ah yes, so it does! Excellent, so this may well be the right 1901 census entry. Thank you.
The main problem will now be to identify where Tom Bedford and the children are by 1911. There don't appear to be any Bedford births in Walsall that would match the missing third child from 1903.