I don't get that Roger - more expensive than the trains previously suggested & still available? (eg £10 out, £7 back. £5 out available on slower trains).
A&H, your public transport option is ludicrous for a 110mile trip but, if you were determined, and time on your side, you could get a £7.80 day return (train) to Sheffield (27mins) and then pick up a megabus to Brum, varying between 105mins & 135mins, currently £5e/w for that date.