Tamworth to Aslockton (not via Birmingham), or Tamworth to Grantham (not via Birmingham), are £140.70 for a week, £540.30 for a month and £5,628 for a year. A season ticket allows you to start and end journeys at intermediate stations on permitted routes between the ticket's start and end points.
Interestingly, there's no season fare for Radcliffe (the station before Bingham) either. Or a Tamworth to Nottingham season is £69.70 for a week, and Nottingham to Bingham is £26.10 for a week, so if travel will always be via Nottingham that combination would be £95.80 for a week (and proportionately more for a month or year).