Citing a 'co-student's Bachelor's thesis I am currently in the process of writing my bachelor's thesis. Another student is working on largely the same subject as I am, with a slightly different focus. Is it acceptable for me to reference his thesis in mine? If so, wat would be the proper form for this.
Of course it is acceptable as long as you know what you are referencing.
So as long as you have read her thesis (or the part you are referring to) and you think it belongs in the literature review of your thesis: Do it.

However, if you want to use a result derived by her, I would advice against it, as you can not be sure if it really is correct. If it is not possible to avoid using it you should talk to your supervisor about it.

For the proper form:
@masterthesis (as @Wrzlprmft already pointed out), @thesis (with type = {Bachelor's thesis}  or @unpublished could be an option for you.