You can put a signup form in the summary screen after the actual purchase. The text could be something like “Great, you have bought your tickets and we sent a copy to your email address. If you wish to track them, change your booking later, or , you can set up a ticket book below”. Then show a simple sign up form with textbox for email address (prefilled since you presumably have the email from the purchase), text box for password, and “create my ticket book” button.

The advantage is that people are not forced to sign up, its pretty clear what the benefits/tradeoffs are, and they will be more receptive to signing up after they have already done most of the work. Of course, the whole login system should use email addresses as identificators, i.e. don’t force the user to make up yet another username.