Here in N Wales, Arriva runs most buses and the local trains. Some fares seem high (singles on the bus) while others are quite low considering the mileage possible (if one can stick hours on a bus!)
Single into town is 1.80 (1.30 is minimum fare) on bus, but a day ticket is 3.00 (have not bought one yet as tend to use train), but that 3.00 ticket covers as many trips around town and within the county from town centre bus station on Arriva. Some other firms run, but to tiny number of villages and never need to use them so don't know how they compare.
There's also a regional 'Saver' Arriva bus ticket at 5.50 (for Wales and North West) so could go from Wrexham to Barmouth / Aberystwyth, or off to Liverpool / Manchester / places in Cheshire/Lancashire or along the northern coast to Rhyl, Bangor and Holyhead (Anglesey).
Not sure if I could get back the same day to be frank, but considering the single fare on the train from Wrexham to Chester (10 miles) is 4.50, if I paid for a B+B it would probably be cheaper with 2 Saver tickers (one going and one back) than by train!
However, local council helps fund train route near me, so a return is 90p (plus 15 minute walk) and trains run hourly.
I walk to local stores [Iceland, Lidl, Co-Op] (15 minutes), or use train to get into town centre for banks, plus Asda 24h, Sainsburys, Tesco 24h, Aldi, Argos stores, BHS, M+S, etc, etc.