I've been using warfarin for 25 years and don't recall nosebleeds. If you've got a meter, it probably wouldn't hurt to check your INR to confirm that it's in range when these (at least one or two) nosebleeds occur.
The sinus rinse mentioned by Dick is probably the one from NeilMed. It's available at RiteAid. If you belong to Costco, they've got the best deal for these - two (or three?) bottles, 250 packets of the sodium chloride/sodium bicarbonate power that is used to mix the rinse solution, and a can of spray to moisten your sinuses. If you don't belong to Costco, I found that the packets are less expensive at Target than they are at Rite Aid.
I've stopped using the sinus rinse - not because it didn't help, but because I'm basically a bit lazy about self-care, and it's a bit weird putting the bottle in a nostril and squeezing the bottle so that the solution comes out the OTHER nostril.
I may wind up going back to it when I think that I REALLY need it.
I wish you a quick resolution to your nose bleed situation.