Does bitcoin have the potential to be subject to a hard fork where miners are forced to choose which fork they will accept, like Etherum?
Yes, Bitcoin could also be subjected to a hardfork. In fact, there are members of the Bitcoin community that feel so strongly that the blocksize should be increased that they are proposing to do just that:
They are working on a version of Bitcoin that is incompatible in regard to the current consensus rules of Bitcoin forcing a permanent split of the blockchain into two. They surmise that their vision for Bitcoin will have greater support than the road map followed by the Bitcoin Core developers and expect to oust the original chain completely.

As they (IMHO) appear to overestimate the support for their project, I don't expect the latter to come to pass.

As Mindwin has pointed out in the comment rightly so, the Bitcoin blockchain has actually forked before by accident: See march-2013-fork, or Bitcoin Magazine's report.
There have also been previous forking attempts, such as the ones pushed for by Bitcoin-XT and Bitcoin Classic.