On this route, there can be savings to be made by splitting at most of the following: Sheffield, Derby or Birmingham or both, and Cheltenham.
The Bradford-Bristol offpeak return with 16-15 discount is £73.80
Buying separate offpeak returns (anytime returns where OPRs are not available) gives:
Bradford-Sheffield £9.95
Sheffield-Derby £13.65
Derby-Birmingham New St £11.30
Birmingham New St-Cheltenham £16.25
Cheltenham-Bristol Temple Meads £11.75
Total: £62.90
Edit: you could save a little bit more by travelling via Manchester and Newport (South Wales), but the journey times would be lengthy. If you want to check that out, look separately for Bradford-Manchester tickets and then Manchester-Bristol (via Hereford) tickets.