Heater/dehumidifer advice?

I'm hoping a knowledgeable contractor-type person can point me in the right direction here.  I have a large downstairs room, next to the garage, that has a full bath attached.  It's not underground, but feels pretty basementy -- often damp and cool.  I have a split system (heat/cool/dry) that was there when I moved in, but it's old, and the "dry" function only works when the air conditioner (which is literally NEVER needed down there) is on.  What I need is a dehumidifier (turning on/off constantly?) and heat (occasionally), ideally in one unit, but I know that may not be possible. I don't want to empty buckets.  There's a funky little closet on the other side of the bathroom, away from the living space, that would make a good place for the unit(s), but is that too distant to be useful?  Thanks for any advice!