I have something like "DDNOS" ("not quite DID") and have had problems with PTSD-type symptoms, yes its hard to be open with people, and at times i do feel like closing off, so sometimes i guess i must seem more distant, it just takes time to let people in. when it comes to what's going on for her, if she ever finds it hard to connect or be open, its likely something is upsetting one of her alters. i find when parts of me don't want to open up i'll find it physically impossible to do things until ive done a little more to resolve it.
what would she want... ? well in relationships i guess people care for each other and get to know each other, so tho at times she might need a little extra TLC cause of her problems, people with dissociative disorders can and do manage their own lives, even when still in recovery. like everything some days are just harder than others. but im guessing if you have something PD-ish, you need a little extra TLC at times too. i guess she probably wants what everyone else wants from a relationship - to be together, to get to know each other, spend time together, and its fair to say she'd probably want something equal where you both care for each other. i bet you find it hard to really let people in too in some ways if you have a PDish something.
making up for what you have done is easier than not doing it any more - dealing with a PD is hard. i was just talking to someone earlier about slaying dragons, different context, lol but i guess if you don't want to hurt her again you have some dragons to slay! its important to understand how you've acted - and why - but you also need to understand your PD is a problem in just the same way her PTSD/DID is, and if my guesses about PDs are right, possibly not so far unrelated - and if she has a hard time letting people in, she (and her alters) have work to do too.
has she said you were harassing her, or was that you/someone else's advice?
if not, if you want to go for a drink/bite to eat with her or watch a movie, why not just ask? if she hasn't said you're harassing her, it sounds like a good idea, and flowers/chocolates/romantic notes aren't harassment unless she says she doesn't want them. I agree with Sandie, most girls like flowers! if you want to get to a girl's heart, i wouldnt worry about flowers being outrageously expensive, personal will go further. nice red roses always go down well, or if she has DID, maybe a mixed bunch, (that way there's a better chance there's at least one every alter likes!) i like strange and exotic different flowers in different colours, lol
but no one's ever sent/given me flowers 
i think as long as she hasn't said your attention isn't welcome letting her know how you feel and doing things like this - if you want to do them - are a good idea. but sensing the PD thing coming in, at the same time, be careful not to idealise her too much - i'm sure she's not perfect!