The cheaper way getting to Golden Palace Hotel but involves a coach and train transfer.
From the KLIA Airport, you need to get to the KL Sentral station (the airport is 60km away from KL) by coach, which is RM12 per trip. The journey is about 1 hour.
Then, at the KL Sentral station, take the monorail to the Bukit Bintang station. The fare is RM3.70.