I Just cannot move my slave to the milking room or my own room no matter what I do. It just says 'there's no room for her here'. Is this a bug?
It almost sounds like you purchased/captured a slave and are trying to move them directly to the milking room. You can't do that, if that is what you are trying to do.
Your personal bedroom does not count as an available room to house a slave and the same for the milking room itself, which is why the game is telling you 'there's no room for her here'.
You need to have a room set up for your slave or an open slot in a double/quad slave room and move them to that room. You cannot move a slave to a milking room or any room other than slave quarters, they need to be
moved to a slave room and then
assigned the job of being milked.
The other thing you need to check is how many people you have assigned to a particular milking room. If you only have 1 slave, they can work any hours that you set. If you have 4 slaves assigned to work in a milking room, they can work any hours that you set. If you have 5 or more slaves assigned to a single milking room, you need to have them work a different 'shift'. Milking rooms only allow 4 slaves to work at a time, so any slave after the 4th needs to be set to work different hours. So, 4 slaves at 8a-6p is fine, but slave 5 and up needs to work 7pm-4am, there needs to be a 1 hour gap because of the way the game works.