Get out the Sawzall! On the 53MY you have to cut a hatch under the carpet in the hall outside the shower drain. You can't pull up the drain from the shower stall because it's held on by two big threaded nuts on the drain elbow. The end of the elbow under the drain is a hose barb and the hose is clamped to that. The hose runs to a separate shower sump inside the aft bilge next to the bilge pump, but the shower sump has it's own bilge pump. If you want to feel what it's like, the mid-head shower has a hatch plate in the floor of the hall just aft of that shower drain. You can stick your arm in far enough to feel and work on the drain connection, if you're a contortionist.
BTW - How are you sure it's the shower drain getting water in your bilge. There are lots of other likely suspects that will run water in your aft starboard bilge including: the aft head pump, aft head sea strainer, aft head Y valve, starboard rudder packing gland, aft sink sea chest hose, aft bilge pumpout hose, and aft shower pumpout hose. The bilge and shower sump pump hoses run to the port sea chest but their hoses crack where they are bent too tight by the grommets and leak when the pump runs.
Good Luck,
Doug Shuman
1978 53MY