If, as Ron says, my demon is banished but is still bound to me, do I get the binding strength as a bonus if I attempt to re-contact and re-summon my demon?

The Binding strength acts as a bonus in the sorcerer's favor both for the re-Contacting and the re-Summoning. Think of it as a "reality anchor" for the demon. It's the same reason that any demon's Binding strength acts as a bonus (again, regardless of whose favor it's in) when resisting Banishing. [1]

See also: Changing Binding Strength