This thread has not been forgotten. After some careful (but not utterly exhaustive) work a 'cheap' single trip from Bath to Darlington in 1850 would have taken one-and-a-half days and cost about 1 pound, 5 shillings and 6 pence plus an overnight stay in Birmingham, not researched.
Very broadly: GWR Bath-Bristol, 12 miles, leave 2.32p.m., arrive 3.23p.m.. Then Midland Railway Bristol-Birmingham, 90 miles, leave 5.00p.m., arrive 9.45p.m.. Stay overnight.
Day 2 Midland Railway Birmingham-Derby, 49 miles, via Whitacre, leave 7.00a.m., arrive 9.00a.m.. Midland Railway Derby-Normanton, via 'Old Road', not Sheffield, 63 miles, leave 9:20a.m., arrive 12.20p.m.. York & North Midland Railway Normanton-York, 31 miles, leave 12.30p.m., arrive 1.50p.m. (note, no 3rd class on this train, would have to pay for 2nd or wait until following day). York, Newcastle & Berwick Railway York-Darlington, 45 miles, leave 2.15p.m., arrive Darlington 4.10p.m.
An epic test of fortitude. It should have been possible to book a through ticket from Bristol to Darlington during the first day's break. Great Western not in Railway Clearing House at that stage. Bradshaw shows some specific point-to-point fares and these have been added to a 'penny-per-mile' for other sections with an estimate for 2nd class Normanton-York. In general terms there was only one train with 3rd class on each route per day at that time. It would have been possible to sleep rough at Normanton and catch a train with 4th class (!) from Normanton to York the following morning and save a few pennies, then the same York-Darlington connection as above.
This has not been subject to exhaustive checking but I hope that it gives a broad idea.