I’ve been confused by the distinction between these two species for a while. I find existing keys unhelpful. Here’s the relevant couplet from the current Jepson eFlora key:
30. Leaves generally withered in flower; perianth red-purple, rigid-keeled, ± shiny in fruit, tip margins inrolled, parts with a purple crescent adaxially just above base — Allium campanulatum
30′ Leaves generally not withered in flower; perianth white or pink to rose-purple, not keeled, papery in fruit, tip margins ± flat, parts without darker crescent adaxially — Allium bisceptrum (and Allium membranaceum)
And the couplet from the Flora of North America:
58 Leaves usually beginning to wither from tip by anthesis; tepals rigid (not papery), ± shiny in fruit, strongly involute at tip, carinate. — Allium campanulatum
58 Leaves usually green at anthesis; tepals papery (not rigid and shiny) in fruit, not strongly involute, not carinate. — Allium bisceptrum (and Allium membranaceum)
Taking the characters from the two keys in order, my impression is:
Leaves withering by flowering: There may be a difference in averages between the two, but if so I can’t tell. Certainly both frequently do have leaves withered by flowering.
Perianth color: There definitely is a difference in averages, with Allium campanulatum usually darker. However, there is too much overlap for this to be reliable.
Perianth rigid-keeled, ± shiny in fruit vs. not keeled, papery: I can not make out any distinction between the two in this feature.
Perianth margins involute vs. flat toward the tip: I can not make out any distinction between the two in this feature.
Tepals with or without a dark crescent near the base adaxially: Allium campanulatum almost always has this crescent, Allium bisceptrum has it perhaps half the time.
My experience of the two is almost entirely via images on iNaturalist. It’s entirely possible that these are all good features on herbarium specimens, and simply do not work well, or are difficult for me to interpret, on live plants. Nonetheless, I find only one of these features useful (the dark crescent on the tepals), and that one only partially. Yesterday, though, I was looking at some iNaturalist observations from areas where only Allium campanulatum should be present, and areas where only Allium bisceptrum should be present, and noticed some other differences that are much more evident and useful to me when looking at pictures of live plants. Geography is, of course, also useful, although relying on it tends to raise suspicion that one is not distinguishing meaningful taxa. I summarize my current understanding in the couplet below:
Stamens remaining straight and erect throughout development; ovary crests dark green; pedicels green, strongly contrasting at the receptacle with the pink to whitish bases (abaxial surface) of the tepals; tepals with or without a darker band near the base (adaxial surface); plants of the east base of the Sierra Nevada and eastward in Nevada, Idaho, Utah, Arizona, and the western edge of New Mexico — Allium bisceptrum
Stamens appressed to the petals before dehiscence, curling over the ovary after; ovary crests dark red; pedicels not strongly contrasting with the bases (abaxial surface) of the tepals at the receptacle, usually purplish or grayish, if green then the bases of the tepals also somewhat greenish; tepals with a darker band near the base (adaxial surface); plants of the Sierra Nevada, south to the transverse ranges, and north through northwestern California and central Oregon — Allium campanulatum
Linked are some typical Allium campanulatum, as well as some typical Allium bisceptrum.
The stamens seem to be the most reliable character, if visible in the available pictures. The tepal crescent is useful when absent, otherwise uninformative. The other two seem to work the majority of the time, but neither seems reliable on its own. One might give stamens two or three times the weight of these two, the tepal crescent the same weight when absent, and treat the set of characters as a vote in which unanimity is pleasant but not necessarily expected. There are still some plants I can’t confidently assign to either species, though, and the color features entirely fail in central Arizona, where Allium bisceptrum is dark-flowered.