How much does a bookkeeper who's also a BAS agent charge or cost per hour?
A lot of bookkeepers offer a package nowadays. Eg: a starter package for new businesses or businesses who want to establish a new accounting software. They will install, configure, transfer your books and get everything up and running including training. This will usually be a fixed price package.
If you're looking at hours, it really varies. Since you're asking for a BAS agent also, it means you want someone to do your BAS too on top of your day-to-day accounts. That can go up to $50 an hour.
At the end of the day, you need someone who is proactive and who you can communicate easily because your company's finances depend on this relationship. Your bookkeeper and accountant should also work closely together (ideally).
Hope that helps.