Everything you need to know from a regs POV are here:
https://www.planningportal.gov.uk/buildingregulations/approveddocuments/parth/approved
(Part H)
If your joists ran front to back:
The minimum slope of any drain inside is 18mm fall per metre (Dia 3,
Page 9 in the above doc).
So if you have about 5" to play with (50mm pipe in 8" joists) yoi have a
max run of about 7m.
In practise you can get away with a little less (I did) on 50mm pipe as
long as it is consistently falling (no "dips" that trap scunge) and you
have rodding access just in case. I'd say 10m is not really a problem
but it's not quite up to Part H.
So Bath/basin/shower no problem - there's plenty of fall available
assuming 8" joists. I would use 50mm pipe for the main run and include
an allowance to let it expand (uPVC does, a lot, when hot water goes
down it). This could be achieved where it does the 90 degree bend to
come up through the bathroom floor - allow that entry to be sloppy to
allow movement.
Toilet - you didn't mention, but I wouldn't. Less fall to play with and
you really do want a decent fall on soil pipe.
If your joists run counter, then you have really 2 solutions:
1) Sump+pump (like saniflo but less horrible). This is a standard
solution but it's not my favorite.
2) Drop 50mm pipe down through the ceiling and run it along the room
wall front to back. Box it in. This is actually a reasonably stadard
solution.
HTH
Tim