ImageMagick: Bold and Italic Fonts?

Try font name with hyphens: -font "Arial-Bold-Italic" - it worked on my Windows 7 (like you, I couldn't make -style option working). Order of styles (Bold-Italic) is important here.

To see all the fonts available to ImageMagick, use convert -list font (and additionally maybe >C:\fonts.txt, because the list is usually very long).