Will targeting images from another site use less bandwith than uploading the images to server and calling in <img> tag?

Yes, definitely. It will load only like 50 bytes of code if you access the image from another site. If you access the image from your own server, it will be that 50 bytes AND the size of the image itself coming from your bandwidth.

However, do not just post an image from someone else's site onto your own. That is rude as it takes up the other person's bandwidth. If you want to upload image to another site other then your own, then you should upload them to a site that is made to host images for people, just as Photobucket, Imageshack, or xs.to

The problem with using external hosts is that they do not provide any kind of guarantee that the image will not be deleted or dropped.

We are using the images of tiles from our supplier to show customers in our online showroom.

It's fine if you have an agreement to do so with the other site. Also bear in mind that if their site is down or inaccessible the images won't display and the page load time will suffer. In all honesty it is far better to serve the images from your own server.

I agree with Blue Dreamer. Using photobucket or other image hosts is unprofessional. I wouldn't want someone to click on one of my images and be taken to another site which lets them know it's 'free' image hosting. It's advertisement for them and makes you look cheap but if that's what you're going for then to each is own.

I would just make sure your images are 'saved for web' correctly and the right size for load time.