Be very careful with these positions. The admin/bookkeeper, in my opinion and >20 years as Sr/Exec admin, they are looking for 2 positions in one job. Now, some smaller companies combine the jobs with 50/50 to each title; however, my experience has been that these are 2 full time jobs. Been there, done that. My rule of thumb is to ask during the interview, what an administrative assistantge is bookkeeper, what level of bookeeping, etc. I do have plenty of budget and financial validation experience, however, I tell them I do not have financial training.
Now if you've had some bookkeeping experience and like the rest of the job - maybe, as part of your package, you can work the job and have them pay for "further education" to cover things you aren't familiar with, ie, payroll, taxes, etc.
If that is not your thing, you may need to look elsewhere. Taking a job with the intent of learning bookkeeping "on the job" could be futile. Best of luck.