No, you don't, at least not for the bank account. You need the tax number from the Finanzamt and the confirmation that you're freelance but that's a different thing.

In any case the registration at the Gewerbeamt (Gewerbeschein) is a different beast than the contract and paperwork needed to form a company. In some cases freelancers are required to register and in some cases companies can be exempt. It's basically a license to do business. If you register you need to pay Gewerbesteuer which can be costly (you can deduct that from you income taxes but often not in full).

So if you can freelance instead of registering a Gewerbe for a single person, do so, by all means. Talk to a tax accountant to know if you really need to register.