It has been a few years, but we just took a taxi and it was pretty easy. It took about 25-30 minutes. I dont remember the cost, but I would have if it was exhorbitant.
The hotel is very nice. They gave us a 9th floor (top floor) room with a balcony. The lounge is one floor below, but from our balcony we could get the free wifi signal from the lounge.
Take a cab, if you have US, going to the Marriott in BA would be about $30 (which includes a healthy tip).
If you're looking to save cash... I have to say the Hilton is significantly cheaper (nearly half). However, I would still take the time to visit the Marriott in BA as it's awesome. It's about 100yrs old and fairly well kept. Take time to look at all of the 'relics' they have around the hotel, it's like a museum. For sure check out the nice selection of meat knives they have ;-)