It sometimes happens that I need to make a small change to just one page of my website.
Is there a way of publishing / uploading just the page that I have changed? I have a fairly large site and it seems a waste of bandwidth and time to republish the whole site every time.

Even though it appears that VSD is uploading everything, it's actually comparing pages to see what has changed. This way it only uploadeds the changed content.
You could use an external ftp client. You will still need to know all the files VSD generates that need to be uploaded.
So don't yell at VSD if your site doesn't appear correctly.

If you are only changing text you should be fine to use Eric's suggestion. If you change anything including positions of the images, especially if they overlap, you should republish with VSD. I am not sure if you noticed but VSD renames most images to a number so if you don't use it to publish it could change one of the image names and everything will be out of sync.