I don't think that your background is actually very unusual. I also majored in cognitive science, and worked for 2 years doing HCI research at a large technology corporation. I've met a number of HCI researchers during my undergrad and at work to know that there is a lot of psychology and ethnography involved, for which a formal computer science background is not necessary. As a field, HCI is very interdisciplinary and cognitive science involved, so I don't think there is any disconnect.
If you're mostly interested in teaching, you could easily get an MS and become an instructor. If you're more interested in doing research then you may want the PhD, but I don't consider this a light decision, especially if you haven't actually worked in a research position. Working in research can be very different from working elsewhere. I agree with starmaker--see if you can find a pre-doc/post-bac program of some sort that will give you CS and/or research experience so that you can figure out if this is something you'd actually like to do. My 2 year contract was a pre-doc program and it was extremely valuable--I'm looking at MS programs now.
You should definitely consider having a letter of reference from an employer. It's nice to have glowing recommendations from your professors, but it's better to have a wider variety of sources to give you glowing recoommendations.