Not entire sure of the idea that Bubblegum served as some sort of guardian for Marceline when she was younger. Marceline kept mentioning about how Bubblegum made her want to change in some aspect and how she thinks that Bubblegum wanted her to be perfect. It gives off a relationship vibe in that sometimes when one is in a relationship, their partner may want to change certain aspects about the other that they don't like (Like the adage of a nice girl dating a "bad boy" and wanting to change him). I think that fits more about how their relationship might have been, with Marceline feeling like she wasn't good enough for Bubblegum and Bubblegum may have been wanting to change something about Marceline that she thought was insignificant, but to Marceline was very important.
A small theory that I have been messing around with is that sometime in the past Bubblegum and Marceline were an item and true to Bubblegum's scientific disposition, she developed a cure for vampirism (Thinking of it as some sort of disease), hoping to make Marceline human again and not having to always to be with her only at night and other positives that come with being human. Unfortunately, Marceline doesn't take it as well as she hoped shewould, stating that she likes who she is and doesn't want to change, feeling a bit insecure and that Bubblegum doesn't like her for who she is. She probably didn't like the idea of Bubblegum trying to change her and wanting her to fit into this perfect mold and Bubblegum didn't help by being stuck in her scientific mindset (Thinking that everything that can be fixed, should be) and the two just had a falling out.
Most is just from the lyrics in I'm Just Your Problem. From the sound of it, Marceline probably felt that Bubblegum was being who she is, thinking that she is always right and tried to change her in some capacity and Marceline didn't like the idea that what she was, wasn't good enough for her. But even then, she still had those feelings for her and probably still wants her (Lyrics like I want to drink the red out of your pretty pink face sort of lend itself to that kind of thinking.
Another theory is a more simpler one in that, Bubblegum probably doesn't like that Marceline doesn't worship the ground she walks on and treat her like a goddess like everyone else and it just bugs the crap out of her. Since she is royalty, she probably expects to be treated a certain way and Marceline simply just won't comply, loving how she gets under her skin and she believes deep down that Bubblegum wants her more that she cares to admit, but as a Princess, such thinking is forbidden. Bubblegum may be sweet and kind, but she probably still demands respect from her subjects, even Marceline. But what bugs Marceline is that that same attention isn't reciprocated. Bubblegum thinks that by ignoring Marceline, it means she won't have to acknowledge those feelings, and Marceline absolutely hates that, because it makes her feel like she doesn't even treat her like a person. My guess is that at one point, Bubblegum realized she was getting too close to Marceline and that it would be best to simply ignore her feelings and ignore the scrutiny she would have to face. She feels ignored and just wants Bubblegum to acknowledge her again and stop ignoring her like she doesn't exist.
Although given Bubblegum's reaction to Marceline's song, she probably feels like Marceline couldn't be more wrong about her and that she still cares about her, she just doesn't show it as often as she would like to and probably feels some guilt for that. But deep down, she probably doesn't feel like she did anything wrong and just wanted Marceline to change for her (Probably giving her an ultimatum) and feeling like what she requested from her wasn't asking too much. She probably didn't like Marceline's attitude and wanted her to shape up and fly right if she wanted to continue being with her, making Marceline feel like she was no better than any of her servants if she did comply.
The door's reaction to Marecline is pretty interesting as well. As we know, it only responds to the truth and it only stopped responding to Marceline when she mentioned wanting to bury Bubblegum into the ground. The door probably stopped because in truth, Marceline wanted to do nothing like that to her and just wanted to make up with her and probably more (Drink the red from your face probably means kissing her).
By the end of the episode, it looks as if they both realize how wrong they had been and show signs of willing to open up to each other again. The t-shirt part was especially cute.
Again, these are just some theories. If I were a writer for the show, that's how I'd probably frame their relationship, given the information present.
