First off, this is an excellent question.
All ladybeetles have jaws and the ability to bite, but some certainly seem to do so more often.
I’m fond of this question for more than that, though.
I got my start in entomology as a highschooler in South Dakota. Dr. Louis Hesler, a USDA lab scientist who specialized on ladybeetles took me under his wing, and helped me learn to identify them. I specialized in dissecting and identifying tiny ladybeetle species, often less than 1/10th of an inch long. That was the first time in my life that I felt I was doing work that couldn’t be easily replaced, and it was an addictive feeling.
If you have ladybeetles in your home, and have been bitten by them, I’d expect them to be Multicolored Asian Ladybeetles. Other ladybeetles are quite capable of biting, too, even if they don’t do so terribly often.
It’s more a question of what kind of ladybeetles we regularly encounter in our homes.
This past autumn I saw just over a dozen species of ladybeetles around our place… and I wasn’t searching for them. For comparison, South Dakota is currently known to have 80 species of ladybeetles. Chances are good that Montana has a similar or higher number. Despite all the ladybeetle species we had outdoors this summer, the only species I’ve seen in our home this winter is the Multicolored Asian Ladybeetle.
Why are these beetles in our homes? To avoid the cold weather.
While most ladybeetles need to avoid freezing to survive winter, not all do so in the same way.
European ladybeetles, such as the Seven-Spotted Ladybird Beetle (now common in North America as well) often overwinter in leaf litter. New World ladybeetles, such as the Convergent Ladybeetle, tend to overwinter inside rotting trees, much like Cluster Flies further from human structures do. Smaller ladybeetles are known to overwinter inside ant burrows, feeding on their larvae through the winter.
The Multicolored Asian Ladybeetle, has a different history, though. This species has lived alongside soybean farming for ages – the soybean was domesticated in the 11th Century BC. The Asian Ladybeetle’s ancestors overwintered in barns after the soybean harvests, and its descendants seek out shelter in human-made structures as well… It is this behavior that brings them into conflict with humans more than other species of ladybeetle.
Not all entomologists think that Asian Ladybeetles are likely to bite.
This write-up found that only about 1/4 of Asian Ladybeetles bit the author when given the opportunity… When not removed from his hands after they began biting, the Asian Ladybeetles happily feed on him for about a half hour. I suspect few people besides entomologists have personally experienced this phenomenon, however. One can see how similar behavior on fruits can quickly make these into pests.
How can I prevent the Asian Ladybeetles from invading my home in the winter?
Well, I can tell you what doesn’t work, and what ostensibly should work.
Putting up “Ladybug Houses” will not work at all. These beetles aren’t stupid – they can tell it’s warmer in your home than in the ladybug house, so your home will be their clear preference for winter quarters.
It’s theoretically possible to caulk your house so well that insects won’t be able to get inside. In practice, I don’t think this is viable at all. Good luck getting all those 1/16th inch cracks closed! There will always be a few tiny gaps that you miss, and the insects will invite themselves in to the warmth.
If you feel the need to remove your ladybeetle infestation, I’d suggest vacuuming. With a good suction attachment, you’ll be able to remove the Asian Ladybeetles without smushing them and making stains. I’d suggest emptying the vacuum bag promptly, or they’ll crawl out and continue on their merry way. Purdue Extension advocates using socks when vacuuming bugs.
Vacuuming them up can also be a wise idea if you’ve got a dog who likes to eat ladybeetles. Consuming sufficiently large quantities of ladybeetles, regardless of the species, can make your pets sick. But, as Paracelsus said, “The dose makes the poison”. It takes a special dog to eat one ladybeetle and decide to follow it up with fifteen more. I suspect your beasties may be a bit more discerning.

I’ve observed many of these species here in Montana as well.