Is it possible to place a filled waterbucket in a dispenser using a command, like /fill or something like that?
Why don't you just put it in a dispenser yourself xD
Because its a scripted building with hundreds of dispensers.
I know that, when using worldedit, replicating the dispenser with //stack will also fill the newly created ones with the same items. I don't know how to define what they will be filled with without having at least one already there, though.
You can use
replaceitem block <x> <y> <z> <slot> <item> [amount] [data] [dataTag]
to place an item inside any tile entities (chests, dispensers, etc.)