Not sure, if you have a railcard but it's only £9.75 RTN from Heworth to Marton, where you can change onto the 63 (Arriva) for 10 minutes which would be £4.

Only slightly more than an Explorer at £12.90 but it's a much more pleasant journey imo, than been stuck on buses all day. Sure if you're seeing a friend or something you could blag a lift to the station as it's out of any busy town centres.