is there a good place to pick up packaged, ideally latex free rubber gloves? We had a bleed incident at work yesterday (I wasn't around) but thinking it might be something I should stash in my bag/desk/etc since our work kits are often lacking supplies or generally missing.

Nitrile gloves. Box of 100. $20ish available most car-part, hardware, department stores.

@TNZ71
and just stuff them into a small ziplock?

I got one of the PPE sets from NAR but that has a mask and packaged sterile gloves. Less worried about them for this case but didn't know if there was a pre-rolled solution for first aid kits

Make sure you rotate them. Gloves don't have a long shelf life

This is what I buy for emptying the trash and stuff at our car wash... There are some truly nasty folks out there.

If needed. I keep a box in the garage for working with oily greasy things. I keep some in laundry room for caustic cleaners and I keep a box in the kitchen, comes in handy when pulling a hot shoulder apart after it rest for an hour and still wants to scald your bare hands.

Carry this on my duty belt, gloves hold up for a couple of months before have to be replaced.

https://www.amazon.com/dp/B08H7CV5J7?tag=arfcom00-20

Nitrile Is what you Need, no Need for sterile ones. As suggested, usually they come in bixes of 45/50 pairs. There are also small ziplock bags with 10 pairs of rolled ones (single pair rolled and held by a paper strap), but they are expensive, 1$ every pair.

There are however small refillable plastic dispensers that hold 5 pairs and have a belt clip and a velcro attachment, you can keep in your desk and put It on the belt. Soldi by mueller or other brands.

Also there Is a molle pouch with an elastic mouth
to retrieve gloves, the condor emt glove pouch, which Is a Copy of the older emdom Grobes pouch. Also 5.11 makes a similar design.

50-100 for $10-14 depending on thickness and glove count at Harbor Freight. The ones you get from an auto parts place or wherever are made in china anyway