The thing is that I still want BW to give me the possibility to choose a site to fill in (so I do need the popup). It is just that sometimes I need it out of the way, and there is no gesture for that (such as sliding it to the side for instance, or long pressing to make it go away)
Are you referring to the popup created by the autofill service that is integrated in Android (https://developer.android.com/guide/topics/text/autofill)? In that case you can activate the inline autofill functionality (assuming that your keyboard supports that) so that no popup will show up.