Micki!, yes it is very poisonous and very dangerous if you get bite.
It's poison spreads out from the infected area, causing the skin and muscle to rot. If your bitten by one and don't get it checked out you could end up with a hole in your body.
An old guy who lives down by my parents was bitten by one, he didn't go to the doctor in time. He was a hole in the back of his leg about three inches wide.
And if gone unchecked it can get my worse, leading to blood poisoning and infection.
I've been bitten by a brown recluse twice. First time I got blood poisoning and had to go to the doctor. Second time we caught it quick enough nothing came from it. Living out here in Kansas in the country it's very easy to get bitten by them.
oakman, I would strongly suggest you just kill the fucking thing. While it may remain under your bed most of the time, the time it would come out would be at night.
Most people are bitten in their beds as they sleep, they love beds as they are dark and usually cool places.

But if your dead set on capturing it... just be careful.
And if you notice any new marks on your body check them out. A brown recluse's bite mark is usually triangular in shape.