This is Dave with Bullhorn's API Support Team, and I will be assisting you with your inquiry into the requirement of the email field for a Bullhorn user.
An email address is not required, unless the client has email integration set up and the new user will need to track emails. At that point, the In-Bound Email setting on the user profile should be enabled. This is not typically the case if you are enabling API users, but is common if you are to set up standard Bullhorn users.
Hopefully this provides the insight you need, but please let us know if you need anything else.
Enterprise Support Analyst
Bullhorn Support Contact Numbers
UK: 44 800 032 2848
Australia: 61 28 073 5089