I did some research, and I can't find a definitive style guide, but here are some opinions:
Writing Dialogue for a Deaf Character -- Absolute Write Water Cooler
Advice on Writing Dialogue With Signing Characters
(Caution: NSFW language in site name)
And here's an interesting one on "gloss," or the literal transcription of ASL:
Gloss in American Sign Language (ASL)
The thing that comes out most clearly is that ASL has a very different grammar and structure from spoken English, and that the basic vocabulary words are heavily modified by facial expression and body language. So a literal transcription of the words would sound very strange and incomplete -- much as a verbatim translation of any foreign language into English would be.
(It often annoys me that when the media cover gorillas and chimps that have learned sign language, they always translate it verbatim so that it reads like a childish pidgin, whereas if they translated the exact same signs from a human speaker, they'd render it into proper English grammar. It's a double standard that makes the apes' communication sound cruder than it probably is.)
So my preference would still be to treat it the way you'd treat any foreign language that you were interpreting into English for the reader. A lot of people in that first link recommend using italics, and apparently some books have done it that way; but the normal convention is to use italics for untranslated foreign words and Roman text in quotes for translated speech. So I'd prefer to do it that way. But it would help to be familiar enough with ASL communication to be able to describe at least some of the gestures and body language for embellishment, as suggested in the second link.