The bookkeeper shouldn't be telling you what to claim on your W4, but they do have the authority to reject and ignore an obviously fraudulent claim.
However, their advice is the "safe" approach. Claiming Single with 0 allowances means the highest tax withholding rate and the highest chance you'll cover your tax liability and get a refund and not owe the IRS. The downside is that you usually have too much withheld which means you are effectively giving the IRS an interest-free loan.
But its your choice whether to take this "safe" approach or to claim more allowances at the risk of owing.
Also, if you expect your total earnings for the year to be less than $12,000 you can safely claim exempt (if you had no tax liability last year), because your tax liability will be $0.
So the bottom line is that its really up to you. If you want to take the safe approach and don't mind having more withheld from your pachecks to ensure you get a refund, then just let the bookkeeper set you at Single-0.
If you really want to claim more allowances to get bigger paychecks but a smaller refund or potentially owe on your tax refund, then turn in a W4 that represents the allowances you want to claim, and tell the bookkeeper that its your choice and she needs to honor your W4.