bmi hotels referred to booking hotels via the bmi website (basically a bmi branded Expedia portal).

Their partnership with Hilton is still ongoing for the moment.

So the best way to earn Avios with Hilton is to:

Book the hotel via the bmi online shopping portal for the chance of some bonus miles. (4 miles / £)

Make sure your bmi number is in your reservation. (1000 miles / night)

Before your stay starts check that the bmi/Hilton partnership is still active. If it's not you can change the number in your reservation to BA at checkin or any time before check-out.