Hi there, Bouquet uses a background image for the custom header, instead of an img tag within the HTML.
Since background images cannot be scaled effectively for different screen resolutions, this means that header graphics in any themes that use this background method are better off not including any text, as it may get cut off, as you've seen. A decorative, abstract, or photographic image without text works best in these cases.
Alternatively, if you're comfortable with CSS, you might want to look into adding in some custom CSS that hides the custom header on small screens. Here's a guide to CSS media queries to get you started: http://css-tricks.com/snippets/css/media-queries-for-standard-devices/
If you're not comfortable with CSS, you could explore some mobile plugins instead.