Looks like a house spider
I know that. I want to know the species.
Looks like a Woodlouse Hunter Dysdera crocata. https://bugguide.net/node/view/3388 Common throughout the US, virtually harmless to humans, but great pest control
Would it bite ? Should i let it be next time ?
Almost all spiders will bite given enough provocation, but they mostly prefer to escape. The bite would hurt, but their venom is not considered medically significant. A good rule of thumb is to generally let all spiders be, since they are pretty fragile creatures.