Bathroom venting options

I just installed a fan in my home's main bathroom, and am looking at options for allowing incoming air to replace the air being vented out of the bathroom. The door forms a fairly good seal with the hallway carpet, so right now there is not a lot of air coming in when the fan is on. I'd rather not shave the bottom of the door. The idea I'm thinking of doing is to install a short piece of ducting to the basement (this is a first-floor bathroom), with a cold air return register cover over the opening in the bathroom. This will provide plenty of airflow.
Are there any potential problems with this idea? My main concern is that the vent would be close to the furnace and water heater in the basement, potentially causing backdrafting issues. Thanks in advance.

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