Bookkeeping is a Profession
A Creditable, Purposeful, Helpful, Profession
It is more than acceptable and in fact is a strong message to your employers and your client base about who you are and what you do!
Being a bookkeeper means you can charge a fair rate, even a good rate. Professional contract bookkeepers should be charging a minimum of $65 per hour, (simply to equate with an employee on the clerks award).
Bookkeepers using the best technology, streamlining and automating some of those routine data entry tasks should be charging more than what you previously did for these low value tasks.
One could argue that prior to some of the automation we now have, as bookkeepers we charged one rate for everything we did. We probably overcharged for the low value data entry and didn't charge enough for our verification, review and report work. Certainly not enough for your BAS Agent work.
Your rate could easily be greater with some charging up to and beyond $330 per hour for their system analysis, integration, review and reporting.
Arguably this rate is still too low. Accountants doing some of this work are routinely charging more.
Being a Bookkeeper or calling yourself a Bookkeeper does not mean you have to charge less.
It's more than OK to be a Bookkeeper.