Is bright red blood normal during a period? I've never bled like this before.

Probably. Bright red bleeding can be normal but the question here, is this normal for you? What has changed, if this is new for you? The blood a woman sees on her cycle is mostly the lining from the internal uterus mixed with blood. The color is determined by how much blood and how quickly it reaches the outside. The faster, the brighter. Changes can be from a missed pill, or a resolving ovarian cyst.