IMO, "business development" is misleading here.
Someone in biz dev thinks of strategies that grow your business, via things like partnerships, channel acquisition, M&A, etc.
What you're describing is an office operations manager - someone who can handle the day-in/day-out of biz ops like you described above.
You're also looking for someone at the assistant level when that really just sounds like you're saying "we dont have a lot of money". I'd suggest a change of title (business operations manager), and it'd be nice to see the JD you're using so we can help you refine it.