@TyndieRock is right that you can't, as far as I'm aware, apply classes to bootstrap-ui tabs. Any ng-class is stripped and directly adding a class causes bad behavior and it blocks any attempt to inject into it.
I did see an issue posted on github asking for custom css support. So maybe someday.
@TyndieRock's solution gets you closer but doesn't get you all the way. Kudos for finding tab-heading
. Although his syntax is just slightly off.
Here's what I think you'd want:
<tabset>
<tab ng-repeat="tab in tabs">
<tab-heading ng-class="{new:tab.new}">{{tab.title}}</tab-heading>
<div ng-include="tab.page"></div>
</tab>
</tabset>
This will let style the text. But it doesn't work so well for your css content.
You might want to do your own custom tabs. It is a hassle but that'll give you the control you're looking for.