Spoilers if you haven't seen the last episode of Hannibal.
From the moment her character was introduced, Bedelia embodied coldness and detachment...
Some would say it's clinical detachment, but I believe that Bedelia is just detached from her human self. If Hannibal is some sort of fallen angel with a god complex, Bedelia reminds me of an Olympian goddess. She's curious about human creatures, and likes to observ them and even toy with them as a psychiatrist (and we saw her playing that game with her former patient, with Will, and with Hannibal himself when idiscussing his past with Mischa), but emotions are too messy for her. When she had her bitching contest conversation with Will, she used the word "passion". Bedelia is always in control and passion is the opposite of being in control.
That's a big difference between Hannibal and Bedeilia. Hannibal, for all his lack of ethics, mind games and cruelty, is a sensual creature who enjoys "la bonne chère" (good food), refined wine, quality music and fine art in general...and he did like some people too, like Bella Crawford. And of course he's in love with Will. Hannibal is a passionate creature. Bedelia is rather...hollow. She's all suit without any flesh. How could she have scars since she doesn't really have flash? She is, much more than Hannibal, the anti-Will.
Bedelia is beyond that kind of emotions. She may be annoyed and afraid sometimes, but she's mostly detached...except that time with the patient who was supposed to have attacked her according to what was said in season 1. Hannibal sent a patient after he triggered him into swallowing his tongue because he wanted to see what Bedelia would do, and indeed she killed the patient instead of saving him, shoving her whole arm up to the elbow through his throat and pipe - something that is anatomically impossible unless she previously broke his teeth and jaw but we know that the show doesn't really care about the plausibility of its plots!-, but most importantly the fisting/killing made her collapse in a way that was so obviously sexual. Bedelia was swallowed by a beast then, but it wasn't the gentle fiction she talks about in her lectures!
Our new serial killer, Francis Dolarhyde is also a creature of passion. The voices he hears own him, and the tiger scene pointed out how turned on he was by Reba touching the body of the beast. When her hand reached the tiger's mouth the emoition overwhelmed him and he had to bite his own hand (Richard Armitage was great!). Later he was still on fire when he sniffed the painting and consumed it. Tigers or dragons, they are all metaphores of the beast that feels.
Bedelia is not a beast that feels. Hannibal has a lot of control for a serial killer, especially compared to the other serial killers the show depicts but he still has the urge or need to kill and eat...or to see Will or to have Will come to visit him.
So why did Bedelia follow Hannibal on the run? I think she did it partly because she wanted to observ that unsual creature he is, partly because she wanted to see if he would do something that would turn her on again. If Hannibal was familiar with Hell, maybe there would be a new mouth for her to shove her arm into, metaphorically... A Hell mouth of course! BTW am I the only one who thought about Buffy during Bedelia's speech?
Bedelia lived with Hannibal "behind the veil" because it was an interesting place to be, next to the cannibal, but I don't think she really enjoyed anything and when Hannibal came back all covered in bruises, it was her cue to leave and put an end to the experimentation.
Not only did she lie about being iunder Hannibal's chemical thrall in Italy in order to escape troubles...but now she's capitalizing on the lie and giving lectures about it! No wonder that Will was so bitchy to the point of rudeness!
She's so self-satisfied. It amused her to play on Will's jealousy and yet IMO she has no desire to be a part in some triangle, and spoke the language of truth. She was back on her cold Olympian seat when facing Will as if he were a patient.
Hannibal may see some humans as cows or chickens or lambs...but to Bedelia they are all insects, interesting to watch or to push towards certain direction, and so easy to crush.
BTW apparently the line about crushing a wounded bird on the sidewalk comes from something similar
Jodie Foster said in an interview, explaining that she hated weakness...which is quite disturbing.