The reason that Garamond Bold Italic is not available is simply because the font itself does not exist, at least in terms of what Microsoft ships with Windows and Office!
Unfortunately, Microsoft Word and other Office components make believe in the general case that every font has a regular, italic, bold, and bold italic face and provides such options to you whether the actual font exists or not. If such a font doesn't exist, such as in the case of Garamond Bold Italic, what Windows does is that it simulates a bold italic face of Garamond Italic by emboldening the letters for both display and print. If there is no italic face, italics are simulated by obliquing. Sometimes such simulations are “adequate” and very often they are absolutely terrible looking!
Adobe Illustrator and other serious graphic arts programs including InDesign and Photoshop don't commit such typographic travesties.
In your case, if you really want a true Garamond that has real regular, italic, bold, and bold italic faces, you might try Adobe Garamond Pro or Garamond Premiere Pro - both available from Adobe - or other Garamond font families available from other font foundries.
PS: Please post questions about Illustrator in the Illustrator forum.