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="//">
<script type="text/javascript">(function($){   
provider_id: 'bookability',   
business_id: '12345678',        type: 'iframe' // side-button, popup       

<!-- End of Booking Service Script -->