This is very common, especially if you have not been able to speak first-hand to any people who have played with your top or dom in real life. It could mean having a friend staying in the living room while you and the dom play in the bedroom. Once again, honorable tops and doms are not offended by expressions of concern for safety and are happy to try to think up ways to make their bottoms or submissives comfortable. She chose to ignore those bells, though, probably thinking her reactions were normal and that she was just inexperienced. Listen to your internal warning bells and stop things before they get to the point where you will regret what you have done.
Some people recommend playing with a safeword, especially when starting out with a partner.
I tend to like this practice myself, and I would be suspicious of a top or dom who utterly refused ever to play with a bottom or sub who has the right to safeword. However, I would not go so far as to say that playing without safeword with a new partner is necessarily dangerous. I know many honorable tops and doms whose play is the epitome of safety with no need for safewords. I tend to think of safewords as a communication device during play, and since there are many other ways to communicate it is quite possible to arrange for safe play without safewords. This is particularly true if you yourself are a novice at BDSM, in which case you yourself do not know how you will tend to react in a scene, much less have a clear sense about the complex range of practices that devious tops and doms can use to push your limits.