[lumpynose]

I think I've figured it out; I need to have the font-family always be Bitter; e.g.

@font-face {
    font-family: Bitter;
    font-weight: normal;
    font-style: normal;
    src:url(../Fonts/Bitter-Regular.otf);
}

@font-face {
    font-family: Bitter;
    font-weight: bold;
    font-style: normal;
    src:url(../Fonts/Bitter-Bold.otf);
}

@font-face {
    font-family: Bitter;
    font-weight: normal;
    font-style: italic;
    src:url(../Fonts/Bitter-Italic.otf);
}

@font-face {
    font-family: Bitter;
    font-weight: bold;
    font-style: italic;
    src:url(../Fonts/Bitter-BoldItalic.otf);
}

Then my css only needs to be

body {
    font-family: "Bitter", serif;
}

strong, b {
    font-weight: bold;
}

em, i {
    font-style: italic;
}

And I can remove the font-family from the h1, h2, h3.