I think that Jane and Mrs Bennet were closer than Lizzy and Mrs Bennet, so it would be a strong possibility that Jane wanted to see her mother. Or another possibility is that having reared five children, Mrs B would be familiar with illness (probably much more than any of the Bingleys, Darcy, or ever Lizzy) and could truly assess whether Jane's was serious. I think this may have fallen into the "no good deed goes unpunished" category, considering how Mrs B then behaves at Netherfield!