I am thinking about buying used bikes from China, shipping them to the US and selling them online. I would like to sell branded used bikes.
Is this legal? Are there particular copyright or customs issues around such a business?
There is nothing illegal about selling used bikes online.
Importing goods is subject to legal regulation such as customs duties. These goods might even be subject to punitive steel and aluminum tariffs since bike metal could easily be converted to metal for other purposes. And, if the bikes have fake trademarks, they might be interdicted, although the "first sale rule" makes import of bikes with real trademarks legal.
There is nothing remotely related to copyright at issue in your proposal.