On the ex-DUB/ORK routes, there are "special" ex-ROI fares, so the DUB-HEL fare is EUR1000. This books into R class on LHR-HEL and either D class on LGW/LCY-DUB or B class on the LHR-DUB codeshares on EI.

Travelling ex-BFS there are different ex-UK fares, rather than ex-ROI fares, so the fares/rules will be totally different.

Even then, ex-BFS may not allow you to combine a BFS-LHR leg on the EI codeshare with a LHR-XXX booked into the cheaper R or D class. In the case of BFS-HEL, it will not. It gives a full C class fare as the cheapest (which books into C on the BA flight and J on the codeshare on EI). So, it's just that BA has chosen not to offer cheap R class and D class tickets from BFS (via LHR)

FWIW there are R class tickets on the BHD-HEL route, if you travel by MAN. This books into J class on the BHD-MAN flight (codeshare on BE) and R class on the MAN-HEL flight (codeshare on AY). This comes out around £800, and uses a REUNBA fare basis, but not sure ba.com can handle it.