Hi, Jelly
It has been my experience that you, the VA, need to be the proud owner of QB (desktop version). Then you can offer bookkeeping services to as many clients as you would like. If you're sharing files with a client, however, you need to have the same version they have. In other words, if they're still using QB2008, you need to have QB2008. I have clients using everything from QB2006 through QB2009, so I have all four installed on my system!
If your client opts for QB Online, however, then I would make them pay for the subscription. Then you get listed as one of the authorized users. The beauty of the Online version is that you both have access to the "live" file at any time. You can use the file for data entry and reconciliations; they can run reports and check balances -- all at the same time.
HTH!
Deb