You forget that we mostly get to see Asuka from Shinji's perspective, who as a co-worker and flatmate, can't escape being with her in close quarters.
He's also what, through Bully-O-Vision (TM), looks like a perfect target as he'd twist himself into pretzels to avoid people disliking him and is likely to asume he probably deserves any abuse/ that no one would help him (Even though his friends usually take his side and defend him.)
Also, Hikari hasn't watched the show other than the parts she's in and has no idea where Asuka does or doesn't shove her boobs (which I really wish the OP hadn't oversimplified or played for slut-shaming)
As we see in ep 9 she's actually super popular with her classmates and maintains a facade of toughness heroism and perfection in public. That's the Asuka that Hikari knows and decided to be buddies with. None of the other girls visit her at home or try to comfort her after things get though because those connections were highly superficial and Asuka collects friends more than she bonds with them, but she's established as a "popular girl" and flaunts it to Shinji's face, too.
To quote Touji, "Those poor dupes don't know anything about her true self."
Hikari might act bossy as part of her class-rep job but it's the "token responsible sibling" sort of bossy, she's concerned with ppls education and proper procedure, and also a bit old-fashioned.
Same with Misato, really, whom she superficially gets along with but secretly disdains, with the facades disintegrating the more obvious it becomes that Misato & Kaji are back together.
On a less cynical note, if you don't know how vicious Asuka gets behind closed doors, or heck, if she is having a good day, Asuka basically looks like a cool, tough, confident person that it would be cool to be friends with.
Hikari might like that she also takes education seriously and admire Asuka's outspoken nature as someone who, as much as they act strict in a caregiver role, can still be pretty insecure and reserved when it comes to interacting as equals (most evidently seen in her attempts to get Touji's attention)
She's ultimately a very caring person so she was gonna have a more serious interest in a person she considers her a friend and even take her for a bit when the lean times arrive.
She also tries to cheer her up about her unlucky battle outcomes in ep 23 in a way that suggests that Hikari finds her fighting for the common good to be a heroic thing regardless of the results. Asuka wasn't able to perceive this as anything other than "pity that makes everything worse", tho, then again the poor girl had really been put through the meat grinder all the time.
Alas poor Kaworu! I knew him well...
- Essay on the character's roles in each others introspec sequences
- Good faith Analysis of Mari
- Finish ep 8 commentary