Possible deposit methods vary by which sportsbook you sign up with. This includes which country you are betting from. Each book should have at least one deposit option that doesn’t require providing your bank information. Examples of this are Bitcoin, eWallets or prepaid credit cards. However, if sharing personal information is not something you want to do, know that you will be required to submit some personal identification in order to create an account, plus a billing address if you ever want to withdraw funds.
You can find more details on signing up and potential deposit methods here.