Unless you abuse the relationship approval, it's impossible to do that. You would need over a 100 likes to max out the relationship and there is a check between each scene where you can't go higher until you activate their dialogue or personal quests. I doubt you barely spend anytime with her and max her out like that. If you abuse the like system then it's your fault, not Beth.
I did travel with her for a bit, but I've had Nick with me easily 3-4 times as much as Piper. It didn't feel like it was all that long before she hit maxed out approval, and the most common source of "piper liked that" I got was actually lockpicking(since I lock pick everything in sight).
I've had like 3 total conversations with her, one of which got interrupted by super mutants because she decided having it in the middle of the street was a great idea =P
In order for you to start a romace with a character you have to get them to max affinity, flirting doesn't mean you are in a relationship. Until you get the option romance, that is when the player will enter a relationship with that character.
Plus you atleast have to be around the character to start flirting or enter a relationship. In ME after doing mission I just come and speak to whatever companion I'm interest in, I don't actively have to bring that companion with me. I just come and speak to them after all the important stuff has already happened. Plus like I said, ME does not offer that character the option to break it off with the player, they are drones who will love you after you've gotten done agreeing with them within every conversation.
I am in a relationship with her, I'm saying I only actually flirted once to get there.
ME characters basically just go with it as long as you agree with them, but it's not like Fallout 4 companions are a whole lot better. I keep getting approval for my companions just doing stuff around Sanctuary.