I've been through that area in May a couple of times, finding everything from comfy shirtsleeves weather (intense sun at altitude that time of year) to blinding blizzards, sometimes in rapid succession. Riding can be great fun and very scenic, or death-defying. The upshot is that no one can predict what you'll find in early May, and that remains true at least into late April.
At high elevations--which means your entire route--if there are snowbanks along the roads there will be intermittent black ice at night and early morning, regardless of the weather.
If I were you and dead set on riding out of Durango I'd try to leave my options open, either by preparing to wait out bad weather or by heading to lower elevations. That's a good time of year for riding out of Moab, for example--just pay close attention to the high passes which tend to separate major destinations throughout the Rockies and Four Corners region.
Hope that's helpful.
Mark
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