My two cats absolutely refuse to drink out of a bowl of water left next
to their food (or anywhere!), but will only drink from the bathroom
(which is served by the storage tank).  This is ok for one of the cats,
who will happily drink from a small pool of water left in the bath, but
the 5 yr old female will only drink from trickling water from the basin
tap, which, if we're out can be distressing for us (and probably her)
to come home to find her perched on the edge of the bath waiting
patiently.

This is despite putting filtered water next to her food, and the bath
having water in it for the other cat.

Obviously the real concern is when were on holiday, and there's only
someone coming in once a day to feed them.  Recently she's been
refusing to eat her usual wet cat food too, so her trips to the
bathroom basin have become more frequent.

Does anyone have any tips on how I can change my cat's behaviour, or is
it a case of you can't teach an old cat new tricks?