Is it possible to alter the above route to go via Worcester? I'm not familiar with the route, so not sure how practical that is, but the fares from Bedworth (on the Nuneaton to Coventry line) to Worcester are priced by London Midland, so are more reasonable *and* if the outward journey is between 9th April and 2nd May you can take advantage of the LM sale. Even better, you don't need to go via Bedworth, since Bedworth to Worcester is valid via Nuneaton by the shortest route rule. So you can just stay on the train between Leicester and Birmingham and switch ticket validity at Nuneaton. No point in buying Nottingham-Nuneaton though to try and save a bit more though - Nottingham-Bedworth is slightly cheaper!
So,
Nottingham-Bedworth route NOT BIRMINGHAM SVR £17
Bedworth-Worcester Stations LM Rail Sale SVR £6.60
Worcester-Bath Spa route NOT BIRMINGHAM SVR £24
Total £47.60
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Even better would be to forget about the Leicester and Nuneaton route and go direct to Birmingham, splitting at Tamworth instead (Tamworth to Worcester also priced by LM).
Nottingham-Tamworth SVR £13.90
Tamworth-Worcester LM Rail Sale SVR £6.80
Worcester-Bath Spa rte NOT BIRMINGHAM SVR £24.00
Total £44.70