If the property becomes uninhabitable, which doesn't sound the case in this instance, the LL has a duty to rehouse you at his expense - either in another rental property or even in a hotel or B&B until the problem is fixed.
As I said, I dont think this is the case here and, from what you say, it should be able to be fixed without you moving out. However, if there is a lot of disruption, i.e. floors being taken up etc or your bathroom out of use, it might be appropriate for the LL to offer a reduction in rent while the work was ongoing.
Again, from what you say, I dont think the repairs are down to you, unless youve somehow damaged the seal around the shower, which sounds unlikely. There is a responsibility on the tenant though to inform the LL as soon as possible about any problems so that they dont escalate into something worse.