Cilia slide against BB wears itself out pretty quickly, but it's good to remember it as an option. The biggest issue with it is that BB's high risk/reward options don't really favor Double at any point if she fucks up her own commitments. I generally still commit to lugers if I have the meter to convert luger car > gregor as he's not getting out of it if he's committed to brass already, but before I have those meters it's really just waiting for him to fuck up his fullscreen guesses or interrupting his offense with assist calls, reversals, and pbgcs.
Luger Car > DHC being important to have at fullscreen is also why I'd recommend just using fleshstep route confirms and saving meter as opposed to slide > monster.
As for baiting Beat Extends, relatively little harm in empty jumping forward unless they're really committing to wakeup A-Train on a read. If he does bite with BE, you can falling jLK jMK consistently after blocking the beat extend, and in the worst case scenario where you somehow don't get the hit, he's gotta guess on jLK jMK(2) or jLK jMK(1) fast fall > low/throw/block.
If he has a good horizontal assist and doesn't commit to things much, yeah getting in is obnoxious and you're usually doing it on his terms. When you do get in though, he is super susceptible to instant overheads and reversal baits, and people often forget how nasty/prolonged Double's pressure can be with her air normals.
