Can I file my taxes if I haven't received my 1099 for bonus income yet?

You do not have to wait for the form 1099.  File the return including the amount you estimate (or know) to be the gross income amount and include tax withheld, if any.

That depends as we need some additional information.  For example, did you receive the bonus payment in 2022, that is, was that amount actually given to you without any restrictions or conditions.  If yes, then you should report the income on your 2022 return.  If the bonus was paid to you in 2022, do you know if there was any withholding?  If the gross amount was $5,000, but the amount deposited into your account was, for example, $4,000, then that $1,000 difference could be withholding.  But you should confirm any withholding with your company.  

Whether you receive a 1099 or not, you still need to report the income.  If your bonus has not yet been received, but the company intends to report it as if it was paid in 2022, then follow-up with any additional information you can about the nature of your bonus.