Water back up into sink

We have 2 baths "back to back" on second floor separated by a wall. Occasionally when water is run in Bath "A" water appears in the sink of Bath "B". I am in the process of remodeling bath B and have removed all fixtures. I need to place a bucket under the trap for the removed sink because some times when Bath A sink is used the water will overflow in trap on Bath B. While I have things apart is there anything that should be done? I presume both sinks are "connected" to the same drain pipe that extends to the waste line in the cellar.

Thanks in advance.

You have a partial blockage in the drain line they share. The line needs to be snaked out.

Why don't you cap it off and when you put it back together put a wye with a 1 1/2' CLEANOUT PLUG on the upstream end of the two drains.