after few "mistakes" like yours I am also using dark bag. It takes some time to get use to it (especially because of limited space in bag) but it is good and you can work with your films in kitchen daylight watching your wife preparing dinner and helping kids with homework etc.
What appears as bright to you, isn't so to the film, your eye is focusing that light onto your retina, there is nothing focusing it onto a small area of the film, so the intensity is incredibly lower than whats focused by a lens.
I have also been to darkrooms where some light was leaking in. I realized that after 3-5 min. of being in the dark (my first film loading attempts) and it actually felt quite bright. I did't see anything to worry about in my developed film (ISO 400) becasue of the leak. I read somewhere that some photographers the old days have succesfully developed slow film under star light in a moonless night. I believe it all depends on the sensitivity of the film and direction of the light. In a room there is no lens projecting light right on top of the film. One more interesting thing is that it has recently been proven that humans can "see" their hands' movement in total darkness. It is not real vision, just a trick of our brains that enables us to actually use our hands in the dark and have a perception of what we are doing: