I have concluded that Tom Bombadill did know Strider, or at least some other ranger. At any rate, I am sure Strider knew Bombadill. This is why:
#1. At one point, T.B. sayes something about the decendents of old kings who traveled about, protecting the folk in the Shire and lands about.
#2. At the Prancing Pony, Strider referes to T.B. as “Old Bombadill” and does not ask any ?’s.
#3. Also, at the council of Elrond, when the thought of sending the ring to T.B. is mentioned, Strider seems quite familiar with the name, and talks as if T.B. were an old friend, and well known to him.
I am almost to Bree. 4:32. Farewell