York to Penrith will open at 0001 exactly 8 weeks before the date of travel, and that is a route where you absolutely want to split tickets. Depending on whether taking the via Burnley or the Settle route you split at Preston, or Leeds and Carlisle respectively- thus 12 days time.
Via Preston you should get down to £36. Via Settle about £30 with the 2 way split, Via Newcastle about £28 with splits at Newcastle and Carlisle. That is for 2 people with railcard.
It is a shame that the bus times don't really work (it is a 90 minute wait) or you could have changed from train to bus at Kirkby Stephen or Appleby onto the Eden Valley Express bus to Penrith.
Liverpool to Bath my absolute preference would be Liverpool to Euston/Paddington to Bath- fastest, cheapest, far more comfortable in terms of passenger numbers and the train cars.
Or Liverpool to Chester to Newport to Bath for scenery and to avoid a London Change. That route also suffers from overcrowding on the 2 or 3 car sets so if taking that route I would want to put you on one of the 'Gerald' loco hauled trains- whose new rosters need to be identified.
If you need to go via Birmingham then we would need to do a bit of digging and find out which are the 8 car trains on that route, as the normal 4 car trains are not sufficient for passenger numbers and get pretty crowded. There was meant to be help on hand for that summer with extra trains being released from Avanti, but their new trains are behind time, so the cascade is delayed.
EDIT- The 0908 the 1506, 1806 and 1906 from Birmingham to Bristol are the ones which have 8 cars- all the others have 4 or 5 (if lucky) cars. So travel on a London North Western Train LIV-BHX is £15.10 for 2 people with railcard, then the 1506 BHX-Bath via Bristol is £47.60 for two people with railcard- total £62.70 (looking at a date in 6 weeks time).