Well, Bobbi's been around for 50 years and she's never been a Spider-Man supporting character, so it's not really fair to say that her marketability is tied to how sympathetic she comes off in a single run of Amazing Spider-Man. That being said, during that run, she actually has Peter's back the vast majority of the time. Sure, she gives him a hard time when he's being annoying (like when he set up autotune in the car, but come on, wouldn't you?), but she respects him professionally and listens to his hunches:
- She backed him up when he thought Norman Osborn was behind the Goblin Army and helped Spidey go after "Osborn" (even though SHIELD was against it)
- She deceived and quit SHIELD to help Spidey and Silver Sable get her country back
- She understood why he had to destroy Parker Industries when Otto was going to turn it over to Hydra
- She took seriously Peter's suspicions about Humanitech's AI not actually being artificial
If you look back on most of the times that Bobbi actually comes off as unlikable in her interactions with Spider-Man during that time period, they're almost all from either Spider-Man/Deadpool or random event tie-in books.
I think the real reason she didn't shine in that series was because she's not cut out to be a supporting character. She has her own things going on all the time (in fact, she popped in and out of that book and that was generally her explanation; "Oh, I was off rounding up the Zodiac, "I was doing my own thing, I'm not your sidekick," "Oh yeah, I'll be fine, I've got a new job lined up on the West Coast," etc.) and her own history and drive that motivates her. Most of these sidekick-for-a-single-run roles are basically interchangeable, and characters never come off their best in roles like that. That's why Bobbi really needs to either be part of a team again (see how Agents of Wakanda #3-4 gave her a strong narrative) or get her own solo.