What should the size of the background image for my Bookeo booking page be if I do not want it to be tiled?

The background image is shown in the browser, and extends for the size of the page.

The size of the page (which is not the size of the browser window - you could have scrollbars there) depends on how much data needs to be displayed. So it varies. You may want to use a background image that is very high (ex. 3000 pixels) to cover the entire page height without tiling.

Alternatively, consider embedding Bookeo as a widget in your own website. You can then simply use the default background of your website. Click here for instructions.