You will need an Apple ID in order to request a iTunes Connect account (required to publish to iBookstore).
The good news is that you can create a new Apple ID without installing iTunes on you computer. You also don’t need a mac. The only time you need a mac is when you actually upload your ePub file (which we are more than likely doing for you!).
Start the process here:
Once you have a valid Apple ID (which requires they have your credit card info on file), follow these instructions to request a publishers account on iTunes Connect (please note: it can take a week or so for Apple to approve new account requests).