Okay, try this.
Take the going rate, $45k. That is $22.50 per hour. Add in employer taxes on that of 10.2%.
Now adjust for any other benefits that you would normally expect employer to provide - medical or pension plans, etc. For book keeper at $45k, in a small business that may be zero other benefits, normally.
Next, do you need to provide your own special software, computer, other tools or does the employer provide these things? Do you need to rent an office? Do you need to market, advertise, issue invoices or have other "dead" admin time? This is where the contractor rate jumps up, to cover operating overhead.
Lastly, do you need to charge for travel time for part time work. Can you bill that directly? It sounds like you don't need to be in person very often, so I would just ask to tack on 30 minutes (or ?) to your timesheet every time you need to go in.
So, if no other benefits and you don't need to provide a laptop and bookkeeping software, pay for a secure filing cabinet, etc, then you are at $22.50/hr x 1.102 (employer payroll taxes) = $24.80/hr.
At this point, it looks like $25/hr is fine, and competitive, as long as you tack on travel time (if any) and get the employer to pay for any IT costs that are additional to your personal use, and as long as you have some flex with the hours in a week. (people should pay more to have someone on standby for short notice / odd part time hours in a week).
So - just negotiate the "extras" -- travel time, software costs, maybe loan of a laptop.