I'm at the office today, so I don't have the spreadsheet I used to replicate your stat-block in front of me. But, based on what you've described, the Improved Initiative and Weapon Finesse are the base feats a derro gets as a 3 Hit Die creature. One for 1st "level" and one for 3rd "level" as it were. After that, her 7 levels in bard would have added 7 more Hit Dice, picking up another feat at 2nd level bard (because the Hit Dice would jump to 5 total), another at 4th level bard (for 7 total Hit Dice), and your last one at 6th level bard (for 9 total Hit Dice). The 7th level in bard didn't actually gain you another feat, because it just took the total Hit Dice to 10, which doesn't qualify for another feat. Basically, it gets down to two odds (3 racial Hit Dice and 7 Hit Dice from class levels) make an even (10 total Hit Dice) from which to calculate the total feat allotment. And that gets you 5 feats, rather than 6.This drives me crazy! Why are feats based on HD but ability score increases base on level? I completely agree with what Neil is saying here but I hate that ability boosts don't follow the same rules.
Just a pet peeve of mine.
Nerd rage!
I was just looking at the PRD, and it's more clear there how to add the feats than in the Bestiary (unless I'm just missing it...)