We saw this bee and several others in Sentenac Cienega in Barrel Cactus. Each of the everal cactus flowers had one of these bee in or around in. The bee would nestle in pollen or on the side of the petals, take off for a few patrols over the barrel, then lands in the blossom again and stays for a while. This seemed to be definitely male behavior. The first photo is of a male. I am not positive that all three photos are of the exact same bee.
The bee has two cells and arolia are present. When we looked up host plants, we found at least one megachile, Ashmeadiella opuntiae, that is considered as probably restricted in its pollen collecting to cactus flowers. But I know nothing else of this bee.

UPDATE: I think I may have identified this bee to species. Very few bees collect pollen from Desert Barrel Cactus (Ferocactus cylindraceus, previously F. acanthodes), and these male bees were hanging around these barrels in bloom. When I checked my field notes, we noted males diving down into the cluster of stamens; one male actually came up with a female. And so I checked in Krombein et al for Barrel Cactus as a host plant. No Dufourea were listed under either name. And so I checked for synonyms--and found Echinocactus cylindraceus was the original name given to the plant by Engelman. Under this name, among the few bees listed was one Dufourea, #1935: D. echinocacti Timberlake 1939, listed as an apparent oligolege of Echinocactus including E. acanthodes, E. cylindraceus.

In Timberlake, 1939, New species of bees of the genus Dufourea from California, Annals Ent. Soc. of America, XXXII: p. 399-400 is the original description based on 4 specimens, 3 males from Palm Canyon, Riverside Co, and 1 female from a site now in Anza-Borrego maybe 25 miles east of where we saw our bees. Size of males was 9.5 mm, close to our approximate 11 mm. The two traits Timberlake especially points out are the dilated subtriangular front basitarsi and the strongly depressed head which is longer than wide. One of the image shows the head depression, and the last image I just posted, #486631, shows the triangular basitarsi. I think it is very likely that this bee is D echinocacti.