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Would getting a post bacc premed degree after having a liberal arts focused undergrad be able to qualify someone to sit for the patent bar?

What is a "pre-med degree?" You can get a bachelors degree that qualifies under Category A or you can take enough credits to qualify under Category B. The latter is probably easier, especially if you have some science credits already (e.g., gen chem or whatever you have to take as an undergrad).

Why do you want to take the patent bar? A prosecution job (especially life sci) will be hard to get with just the bare reg number and no actual degree(s) in the science field. And the patent bar isn't necessary for litigation unless you want to do IPRs and even then it will probably be a partner signing the pleadings

Agree with other poster. Patent bar is pointless for you; you are basically unhireable in patent pros without at least a bachelors and it isn't 100% necessary in lit. Even if you need it, I would wait, they are re-considering eligibility rules and may make Masters degrees eligible. If they do I would do a cheap (under 10k) MS CS degree. That would be faster and make you very hireable.