[Morwen]

I don't know, I always imagined Gandalf's rejection fo the Ring is out of acknowledgement of the Ring's power, and not necessarily something to do with Gandalf's character. Gandalf seems more frightened of what the Ring would do through him, and the effect it would have, so much so he even fears being tempted to take it:

Eventhough, Gandalf is humble enough to reject it, he fears the temptation, and there must be a reason for his fear? Maybe it is humility which leads Gandalf to his rejection of the Ring, but he definitely distrusts himself if he were to take it, or even asked to take it. Would that suggest a type of pride in Gandalf, or at least a fear that Gandalf (if tempted by the Ring) would give into pride?

I see Gandalf's acknowledgment of the Ring's power as flowing from and directly tied to his character. If he had less humility his attitude might be more akin to that of Saruman who never seems to question his ability to control the Ring should he lay hands on it or Boromir who in confronting Frodo wished to make distinction between possible effects of the Ring on wizards and half elves and men of Minas Tirith such as himself.
I therefore don't see distrust of self as being tied to pride at all. Pride would give rise not to fear of the Ring and its power but to the complete confidence in one's ability to control it. Gandalf doesn't think he can control the Ring. In fact he is very confident that he cannot. And to me it is that, not pride that gives rise to his fear of temptation.

ETA:

Yes, but isn't accepting one's place in the world also a part of humility? Gandalf's (and Faramir's) acknowledgement that they aren't running the show, they can only control what is within their power, and that is their own choices.

I do agree with this