They are not invasive. I'd say they are more like "slow to spread".

Not invasive in my experience. They seem to have good years and bad years around here (NYC suburbs). After getting rid of some nearby invasives, my bloodroot plants did spread a bit but it was not overwhelming and actually very welcome. Some of those same areas later lost some ground. They also disappear for a good part of the year so if you get tired of looking at them they will do you a favor and get lost for a few months in any event.

In the right situation they will seed themselves around. I first planted some about 40 years ago and now I have thousands and thousands. They are also easily divided. I also have the couble and have over a hundred of those and have probably given away at least that many. Each flower may last but a few days, but I have 3 -4 weeks of bloom depending on the site.

"how quickly does Bloodroot spread?"

Not quickly enough.

In my garden, bloodroot will tuck itself between things but is in no way thuglike.

not at all invasive....Interstingly i had thousands of them one year that had seeded themselves about (tiny little ones) and the very next year they were all gone. I have never figured out why...maybe something in the soil but very wierd. If you want to propagate them you can cut the "red" tuber in as many pieces as you wish and plant them and they will be new ones.