You can easily change the style of the booking widget and make it appear as an iframe on your page.
Check this example (note: please take the code which you get from the system).
<!-- Start of Booking Service Script -->
<div style="height: 420px; width: 378px;" id="widget-booknpay"></div>
<script type="text/javascript" src="//my.hakema.net/hakema.js">
</script>
<script type="text/javascript">(function($){
$('#widget-booknpay').Booking
({
provider_id: 'bookability',
business_id: '12345678', type: 'iframe' // side-button, popup
});
})(jQuery);
</script>
<!-- End of Booking Service Script -->