It is easy to add custom CSS to the Beds24 booking page to change it's style.
One of the many things that can be done with CSS is adding a background image.
Because the booking page is a secure page, your background image needs to be hosted on a secure website otherwise the browser may report that parts of the page are not secure.
This simply means hosting it anywhere so it is publicly available using https protocol. You will need to provide your own hosting for the image file.
A google search for "image host with ssl" should provide lots of possibilities.
Once you have the image securely hosted , add the following to the Property Custom CSS setting on the STYLE settings page.
Change the website, directory and filename to point to your image file and it will appear as the background of your booking page.