I use the drybuckets command from DFHack. It seems to empty the well bucket as well as the ones lying about. I think the bucket gets left full when someone is interrupted in the middle of a drink, perhaps by a berserker or an enemy attack. I have only personally seen it happen under chaotic and violent circumstances.
I have two beds in my hospital each with a bucket filled with 7 and the other 8 water... so I was lucky the buckets were left here. It's the only place you want buckets with water. A crippled dwarf can take his own drink if he lands in one of these beds. Buckets with water dropped elsewhere in my fortress I just sell at the depot, but thinking of keeping the materwork quality buckets to use for building wells.
Are you sure?
Whenever I find dehydrated dwarves in my hospital, and no-one bringing them water (or cleaning their wounds), I usually also find my well is "bucket full".
Deconstructing the well and rebuilding it with an empty bucket (often) solves this.
Is this just a coincidence then?
My well buckets say Full and water is delivered to those in the hospital... even those which don't land in the special beds. The main problem you are experiencing is the issue where hospital priorities are rated as very very low importance. So your doctor might perform several other tasks such as drinking, moving stuff/items, going to sleep or taking a break before visiting a patient who is bleeding to death.
What to do....
A) Have your doctors only perform doctor tasks (pink section in dwarf therapist) when any wounded exist or if you believe some dwarves will soon be wounded.
B) Have more than one doctor whenever possible to match advice from A).
C) Have doctors who care about people... a doctor who doesn't give a dammm will take even longer to respond.