Analogously to extraspecial $p$-groups, we define the class of small Frattini $p$-loops and investigate some properties of small Frattini Bol 2-loops. We show that they are related to certain invariant transversals in extraspecial 2-groups. This fact enables us to describe the automorphisms and isomorphisms of small Frattini Bol 2-loops by linear algebraic tools. We use this description to obtain a lower bound for the number of non-isomorphic small Frattini Bol 2-loops of given order.