No chinstraps have survived on medieval bascinets, and for bascinets with mail aventails they would be invisible in contemporary images.
It is well to know that it is quite rare for chin straps to survive on medieval helmets of any kind. There must be thousands of surviving morions, but very few still have their chin straps, although they are well attested in contemporary iconography. And many barbutes and Italian sallets have rivets to attach chinstraps, but no straps.
However, in Christ before Caiphas in The Très Belles Heures of Jean de Berry we see a chinstrap on a small, round skulled bascinet worn without a mail aventail, as well as on a similar, somewhat more pointed helmet covered with scales.
Note how the straps widen to where they attach to the helmet. Surviving sallet straps often split to attach to the helmet at two points on each side, or attach to a shorter strap attached at two points on each side.
There is a reference in Froissart, Vol. III, chapter cxv. to a deed of arms between Sir Thomas Hapurgan, and Sir John des Barres.
It was then the usage (or at least, it seemed to me that it was) that one laced on their bascinet with a mere thong (une seule laniere), so that the point of the lance wouldn't set itself.Froissart records a similar tactic was used by Sir Reginald de Roye against Sir John Holland in a combat before the duke of Lancaster, although in that case the helmets were heaumes.