Hi Douby,
Autocomplete is definitely possible and there are a few plugins available, but, having not used them, I cannot attest to their quality, nor how well they work with BSBITFNM.
I personally would use the jquery-ui-autocomplete js that is in the WordPress core set of scripts. I would load that in (taking note of its dependencies in case it doesn’t work straight off) and either enqueue a script initiating it for the search box or add a script in directly to the html document (and immediately after the search box) using the get_nav_search_box_form
hook. The code examples and api should give a good idea about how to use the autocomplete feature.
I’m marking this topic as resolved as it is not an issue within the remit of this plugin, however, do let me know if you would like further help.
Cheers,
Joe