Since it only happens when you run multiple sources of water at the same time, the sound must be related to the increase flow of water through the pipes. If your water is really cold, it can also contract and expand the pipes and cause a "ticking" sound. But you say it's more like a "tapping" sound.
Since you only hear the tapping noise from the new addition, the problem is most likely that one (or more) sections of pipe is not secured properly, and it is tapping against something, but only when there is sufficient flow through the pipe. This tapping could also be exacerbated by expansion/contraction and changes in pressure, as you open and close valves around the house. If that's the case, you would have to locate the noisy pipe, maybe with some sort of homemade "stethoscope" and tear out a wall to get to it and secure the pipe better.
One other possibility is that it is related to the toilet in your new bathroom or one of your other toilets. Sometimes, when a toilet fill valve is going bad, it makes strange noises in the pipes nearby. Turn off the shutoff valves to all your toilets and see if the noise goes away. If it does, you need to repair or replace the defective toilet fill valve. You'll have to turn them on, one at a time, to find the bad one.