Can someone withdraw funds if they have access to my email and bank statements?

No.

There isn’t a bank that I know of that would allow such an easy walk through to happen. The email and bank statement would provide at best your address, but not any other details. Banks are trained for such. So, in order for the perpetrator to even try to reset or gain access to such, the bank would probably ask the customer information that cannot be supplied simply by having access to the bank statement and email only.

Email is considered a public record and a bank statement is considered an ‘as-requested’ document, meaning it can be requested by third parties. Hence, such information, public, and as-requested documents cannot be used to make a transaction on the account.