AFAIK, the hotels around Heathrow are not allowed to operate an own (free of charge) shuttle bus (I think some hotels operated a shuttle bus many years ago. "There is too much traffic" - therefore it is not allowed anymore).

You can use public bus no 555 from terminal T4 (From terminal T1, T2, T3 you have to go to T4 before). The bus leaves from bus stop no 7 in front of the terminal building. The bus is free of charge.
It stops on the opposite side of the street from the Skyline (5-10min depending on traffic). The bus for the return to terminal T4 stops in front of the Marriott which is next to the Skyline.