Howdy, former Biennoise here, moved away last year, after 30yrs there.
I used to be a committee member of the English Club Biel, admittedly nowadays it is mostly middle aged to elderly members.
I tried to check out the programme on the website unfortunately it hasn't been actualised in some time......but do call the lady listed as president. She is really helpful and might tell you when and where the next gathering is. Might be a start to get to know people.
https://www.englishclubbiel.ch
Sadly, since the last Pickwick Pub closed a few years ago there is no watering hole for Expats as such anymore. Biel used to sport 5 pubs in the 90's and you could be certain to hear English spoken often in any one of them.
Bern is only a 25 Minute train ride away and offers much more for English speaking people.might also be worth checking out