The 23-year-old is available on a free transfer after finding himself forced out of contention at the New Den.
Bull is mainly a leftback but is also capable of playing wingback or on the wing. Last season saw loan spells with Yeovil and Brentford, where he spent four months.
In fact Bull was in the Brentford team that lost 1-0 at Blundell Park in April.
Bull is likely to feature in tomorrow's friendly against Brigg.