A record capacity crowd of 24,021 saw the fifth-round win over Sunderland at Valley Parade and City are keen to repeat that "special atmosphere".
The League One club, which also knocked out Premier League leaders Chelsea in round four, are in the last eight for the first time since 1976.
Under-16 tickets will cost £5, with seniors and students paying £10.
Aston Villa, who play West Midlands rivals West Brom in the first of the BBC's televised games on Saturday, 7 March at 17:30 GMT, are charging between £20-30 for adults and £10 for under-18s.
Manchester United face Arsenal on Monday, 9 March at 19:45 on BBC One. A junior Red Devil will pay £13 to be at Old Trafford, with adult prices ranging from £31 to £53.
Liverpool, who take on Blackburn, also have junior tickets available for £5 with adults paying between £27 and £35 for the tie, which like Bradford's, will be shown by BT Sport.