As of version 1.13.1 there is support for Bootstrap 4: https://developer.snapappointments.com/bootstrap-select/
The implementation remains exactly the same as it was in Bootstrap 3:
This is an example, taken from the site of the link above:
<select class="selectpicker" data-live-search="true">
<option data-tokens="ketchup mustard">Hot Dog, Fries and a Soda</option>
<option data-tokens="mustard">Burger, Shake and a Smile</option>
<option data-tokens="frosting">Sugar, Spice and all things nice</option>
</select>
Live search for the search term 'fro' will only leave the third option visible (because of the data-tokens "frosting").
Don't forget to include the bootstrap-select CDN .css and .js in your project. I am very glad to see this live search become available again, because it comes in very handy when presenting large dropdown lists to the user.