Hello,
I bought an Orchid yesterday from a BBS and low and behold, this morning I wake up to discover what I think is a spider mite infestation. There are whitish webs all over the base of the plant and some between leaves as well. [I'm VERY itchy right now, lol]
The leaves are starting to get spotty and bruised.
I've moved the orchid as far away from my other house plants as possible.

I was wondering if anyone could recommend a good home-made pesticide recipe that will be safe for the plant?
I would really appreciate the help!

Welcome to ATP. I know little about the specific pests of orchids but the American Orchid Society has a couple of articles about mites:

https://www.aos.org/Default.as...
https://www.aos.org/Default.as...

You might want to ask your question on the ATP orchid forum:
http://garden.org/forums/view/...

Thanks!