In both of these cases though, I would have to consciously run a program/open a new file though, correct?

Yes.

While there could always be exceptions and unknown security flaws, it’s extremely unlikely that you’ll get any kind of virus/malware in Linux without consciously choosing to run a sketchy program.

Is running it through Bitdefender first good enough to ensure it’s safe?

It certainly would help, and you could then be pretty sure it’s safe. Nothing is ever entirely 100% safe, though.