I guess that I'd better answer my own question! I was there on September 17.
Yes, there was plenty of water at Bed Springs Crossing on the Deer Springs Trail. The nearby Lily Spring and Rock Spring were flowing across the trail, as well.
There was also water on the Fuller Ridge Trail (PCT) down below at Lower Bed Springs Crossing.
I spent two nights at Little Round Valley, and on my "rest" day I did the 12 mile loop around the mountain, so I have other water news:
I discovered that Deer Springs was dry where it crossed the PCT, but the CCC camp was trail-building full blast and they have a hose running from a small artificial pond up higher in the watercourse to get their water.
Joyce Spring was trickling across the trail just north of Strawberry Junction.
Strawberry Cienega was dry.
Wellmans Cienega was dry at the usual location but there were pools of water at a grassy, marshy area a bit further south.
Don't forget to check out
Hikin' Jim's interactive Map of the San Jacinto Mountains as I used his terminology here. His rating for water sources goes from I (least reliable) to V (perennial).
An aside to Jim: Looks like Joyce Spring should be rated a "III" rather than a "II" - at least this year. The "other" Wellmans Cienega that had water was on what one might call the "South Fork" of Willow Creek, on the map's marshy section directly south of the "C" in Cienega, at about elevation 9180 or so.
And here's a shout out to fellow board member Fred, who I met on the trail not far from Wellmans. Nice meeting you! I'll get a trip report posted in a few weeks or so...