The 18-year-old joined the Robins following a successful trial in the 2019/20 season after coming through Bath City's college programme. He played in National League South for Bath and was highly regarded by supporters.
Wiles-Richards was on the bench for Bristol City's match against Blackburn and helped their Under-23s win Professional Development League South last season.
Hereford's number one keeper, Brad Wade, is still out injured while Cian Tyler cannot play in this Saturday's FA Cup match against Bromsgrove.