I'm not 100% sure this will work with Bootstrap but worth a try - it worked with Remodal.js which can be found on github: http://vodkabears.github.io/remodal/ and it would make sense for the methods to be pretty similar.
To stop the page jumping to the top and also prevent the right shift of content add a class to the body when the modal is fired and set these CSS rules:
body.with-modal {
position: static;
height: auto;
overflow-y: hidden;
}
It's the position:static and the height:auto that combine to stop the jumping of content to the right. The overflow-y:hidden; stops the page from being scrollable behind the modal.
