Try opening up the Creative Cloud app, select Fonts, click on Browse More Fonts, then add Google Bitter to the type kit. I found it here. There are only 6 styles available from Font Kit.
Bitter is an open-source font so I think if you want to try and access all of the styles in the font you will have to deactivate the font from Type Kit and try installing the font using your font manager. I tried it on OSX but only two of the light styles worked in AE. All styles were available in Pages. This tells me that there is something funny going on with the true type font I downloaded from Google Fonts. It is not at all unusual to have problems with free fonts.