The routine of training didn't really change much over time, outside of a gradual increase in intensity, for the Hunter and her apprentice. The two of them did protect the town of Lordran, which they had come to consider their home, from various threats. Something that did change over time however was the relationship between the teacher and student.
The two grew closer, neither being truly aware of the kind of relationship they had until the revelation came to Maria when Elizabeth unknowingly called the Hunter mommy when Maria bid her student good night, letting her student sleep with her, after walking away with a few injuries from a near death experience at the hands of a serial killer known only as Barry the Chopper in Lordran's butcher shop, who's killing spree was finally put to a bloody end at Elizabeth's hands via a semi-accidental shot to the man's groin (she was actually aiming for his hand with his signature oversized meat cleaver, intending to make him drop it), a really hard metallic sucker punch to the face, which could have been straight up lethal if the hidden mechanism Elizabeth accidentally discovered some time ago in her prosthetic that caused a trio of short serrated blades pop out in between the knuckles of her metallic fist had triggered (she almost lost her still fleshy fingers when she discovered the mechanism, she didn't but she did get a few cuts on her fingers), and finally throwing a normal butchers knife, giving the serial killer a literally head splitting headache. The experience was very traumatizing for the young Blood Mage as the Chopper was her first kill that was a human, a deranged serial killer, but a human all the same.
While Maria was surprised by her student unknowingly calling her mommy, she didn't feel offended by it, as she was finally able to figure out what the feeling she had been feeling was. The love a mother felt towards her child, which meant that Elizabeth was viewing her as a mother figure. The Hunter actually felt rather happy about it… and worried that she was doing a bad job considering how… messed up the house of Cainhurst was, like cousins hooking up with other cousins and even more disgusting things, which made it obvious in hindsight why the Blood Mages of the house of Cainhurst (which most of its members were) were more often referred to as Vilebloods. Hell! For all she knew she and Elizabeth could actually be related, albeit distantly, but that was something that she actually doubted. Just because she and Elizabeth had similar features didn't necessarily mean they were related. Though that was something that could be tested with the right rituals… which the Hunter knew of but not how to perform herself, much to her annoyance as she wouldn't have minded if she and Elizabeth were family by blood.