That rather depends on the bus company. Those operated by TfL (Transport for London) are a flat £1.50, Oyster (travel) card or credit debit card only, which you place against the fare reader when you get on. Transfers within an hour are now free.

The exception where TfL buses are free is where your destination is within the Heathrow Free Ride Zone, essentially along the perimeter fence. Most of the hotels along the Bath Road fall into this, and so does Hatton Cross Station (from where the Hilton GI is a short walk). The Ibis is right at the end of the free ride zone, a one minute walk from Harlington Corner (which many buses travel through from Heathrow).

Buses operated by private companies, which also arrive at/depart from Heathrow Central Bus Station, can be more expensive - even approaching the cost of a Hoppa, but they probably still take cash. For the HIX T5, for example, you could catch the (iirc) 75 and get off at the stop over the road.

Buses will almost always be cheaper and quicker than the Hoppa, but if you don't know the system they could be daunting. It's rare that I'd advise this, but in your position and not knowing Heathrow at all well by the sounds of it, you might want to reduce stress and pay a little more for a taxi, certainly from the HIX - the hotel will call you a minicab which probably won't be much more than £10.