Try jumping straight up for the j.D.
For her ground game, basically just learn her pokes and their uses, then incorporate tem into your rush/zoning game. For instance, 2d is a pretty good range sweep, use it at maxrange. j.D is a good air attack because it has a lot of range. 6p is good because it is a good anit-air attack that has a little invincibility on her upper half. 2h is a good attack to use if you can sense an airdash coming.
I use Lust Shaker from time to time. It does decent chip damage, creates space, can be linked into emerald rain, and can be used to stall doing a roll or iron saviour after an attack. For example, I sometimes do a blockstring into standing H, lust shaker, then roll / iron saviour/ set a disc, more rush etc. When doing this, you should be performing it so that the lust shaker barely comes out (like you should only see one strike going upward if you cancel into roll or iron saviour). If you decide to use it to create space, you shouldn't want to press anymore than the default qcb+s. This will give you enough space to do a s disc/fb disc. I hope I explained that well.