I would probably minimize the amount of "locking myself away" if I were you as you'll want feedback sooner rather than later. A major point of DDD is developing a ubiquitous vocabulary (UV) so that the developers and the users are speaking the same language and describing thing the same way. You cannot possibly do this on your own--you have to talk to the domain experts and users to do so.
The UV is the basis of your domain model, so if you've all gotten a grip on the vocabulary, it might be reasonable to develop one (or more) models yourself and present them back to the domain expert to ensure that you are on the same page. It is riskier than simply talking through and building the model together.
Bear in mind that this is really a logical model--you may well need to do a lot of stuff to make it a viable implemented physical model, and the domain expert probably won't care much about that aspect, as long as the physical model still is logically equivalent to your logical domain model.
So, I'd say for the initial logical model, you probably are best off working closely with the DE. If you really can't think with others, try meeting with him for an hour or two a day, and spend the rest of the time writing up what you've agreed upon and any new ideas you have for the model, then revise at the next meeting. But meet daily, to avoid the risk of going too far down the wrong path. Once your logical model is healthy, you might be able to reduce the meetings to a couple a week.
The collaboration between users and the development team is almost always a key factor in successful projects.