Apple Bloom's exact words were "Well, now that we're friends, what if the three of us work together to find out who we are and what we're supposed to be?" This strikes me as much more mature than how you portrayed it.
I also generalized Rainbow Dash/Applejack/Twilight's advice, and Sweetie Bell/Scootaloo's speech. I do that a lot.
Applebloom throws herself into the apple business hoping to get the family-themed cutie mark, and fails miserably.
Applebloom to Dash: My big sister says I'm going to get my cutie mark eventually and these things take time... but I WANT IT NOOOOWWWW!
Rainbow Dash: The key here is to try as many things as possible, as quickly as possible.
Applebloom trains with Rainbow Dash for a while, before switching to Pinkie because she's easier, before trying to get Twilight to force it with magic.
Sweetie Bell and Scootaloo said that being a blank flank didn't make any pony "not special" because they had hidden potential. Basic message being that there's nothing wrong with
not having a cutie mark. Twilight is envious of their upcoming feeling of discovery, and Applejack says they have all the time in the world.
Now Applebloom wants their help with "discovering who she is", which is just another way of saying she still wants the cutie mark. None of the speeches sunk in, they only increased her vocabulary. She's the same pony who just earlier tried to force her cutie mark with magic, although she doesn't have bullying as an excuse anymore (damage done though).
She realizes that they have a lot of undirected potential and suggests they work together to realize it. Even the fact that she doesn't explicitly say 'cutie mark' shows that she realizes the important thing is the journey of self-discovery, not simply having the mark to show it.
Which is why she quits her journey of discovery in Cutie Pox because of lack of results, and then tries to convince Zecora to force the cutie mark with Zebra magic, and when Zecora says no and gives her the same advice almost everyone gives her, she steals the ingredients and tries to do it herself?
And then she's satisfied when her magic fake cutie mark randomly gives her exceptional skill with one of her old toys.
Sure you could assume that they don't care about their cutie marks. However, that doesn't explain why, despite having a friend with the same issue, both ponies were hiding under a table during the party instead of just having a fun time. It took someone being berated in public for them to gain the confidence to be proud of their situation.
They're not friends with Diamond Tiara and Silver Spoon (they're on bad terms actually), and they didn't even go to school with them. Pretty safe to say they weren't invited to the party, and were crashing. They didn't know Applebloom, and revealed themselves after she was insulted for being a blank flank.