This bug was in my bedroom and when I turned on the lights, it moved really fast.
I was able to put it in a jar and I am wondering if I should let it go or flush it down the toilet.
This is probably a type of house centipede, scutigera coleoptrata I think. They are not dangerous for humans and actually helpful because they kill other insects. You can find more about it here:
This type of centipede doesn't bite, as far as I know. There are however other kinds of centipedes (not house centipedes like this one) that bite, which can hurt a lot.
Quotes from wikipedia:
Some species of centipede can be hazardous to humans because of their bite. Although a bite to an adult human is usually very painful and may cause severe swelling, chills, fever, and weakness, it is unlikely to be fatal. Bites can be dangerous to small children and those with allergies to bee stings. The bite of larger centipedes can induce anaphylactic shock in such people. Smaller centipedes usually do not puncture human skin.
The history of a centipede bite is fairly straightforward; the victim typically sees and identifies the characteristic centipede before, or soon after being bitten.
Symptoms which are most likely to develop include:
The wound left by the bite may be accompanied by swelling, redness, and small puncture wounds which may form a circular pattern. This wound may be susceptible to local ulcerations and necrosis.