Versions

We know that alternative versions of historical figures and fictional characters can visit free houses like Neil Gaiman's Inn of the Worlds' End and Poul Anderson's Old Phoenix. Thus, the Sherlock Holmes who visits the Old Phoenix is not necessarily identical with the Holmes who lives in the Time Patrol timeline. Indeed, the Patrol guarding a single mutable timeline and the Old Phoenix existing between many immutable timelines do not seem to belong in the same multiverse - although I postulate a megamultiverse with discrete zones that are not equally accessible.

Unlike Holmes, James Bond receives minimal treatment in Poul Anderson's works. He is mentioned just once as a fictional character in The Corridors Of Time although this would not prevent him from showing up in the Old Phoenix.

In other reading, I have discovered that there are not two but at least three versions of Bond:

the Bond of novels by Ian Fleming, Anthony Horowitz and maybe one or two others;

the Bond of the films plus some film novelizations;

the Bond of other additional novels that are more akin to the films.

I recommend Horowitz.