I have a site with many images that rank on the first page on Google images search for some keywords. I wonder if my bandwidth is used every time someone does a search and my image shows on the Google's search results page (even if the image is not clicked on)?
I think that was the point of the new image search portal they developed. It no longer loads in all the info about the images and displays larger thumbs rather than loading the entire image itself.
Your bandwidth will be used only when someone search on google and come to your site. Just a simple google image search will not load images from your site, they have cached thumbnails for your images that they show... I think
just look at google image search results pages - all the thumbnail images are served from google not from your site
To answer you question, no. If no one will click the thumbnail then the actual image isn't downloaded and you don't burn any bandwidth.