I will be arriving in Gatwick from Cyprus and want to get to Heathrow to a hotel for the overnight, and then to fly to the US the next day! What is the most reliable service?

There is an direct National Express coach between the two airports. No need to pre-book.

http://www.nationalexpress.com/home.aspx

The buses run every 10 minutes or so, taking between 1hr15m and 1hr45m depending on the time of day. Fares currently around 19-20 GBP

"What is the most reliable service? "

There's really no sensible alternative to National Express, except for parties so big it might be cheaper to get a minibus hired.

But many people find staying in London, then getting the tube out the following morning, is more enjoyable than a night stuck in an airport hotel. Depends, of course, on your timings. But airport hotels aren't cheap, and almost all "LHR" hotels are actually further away in time from the terminals than the Paddington Hilton in the centre of town.

Depending on what time you land/depart, flanner's idea is worth considering. If you land early enough to have time to explore a bit of London, do consider staying in the city.

But re the "<i>. . . airport hotels aren't cheap . . . </i>" bit -- using PriceLine one can get 3 or 4 star Heathrow hotels for $45-$55 (£30-£35) a night, which is much better than any hotel in London. Any LHR hotel one might get via priceline are on a Hotel Hoppa route.

I've had overnight layovers in London twice involving a change from LGW and LHR (or vice versa) and I stayed in London. Both times I arrived early enough in the afternoon to at least have dinner in London and that was much more pleasant than an airport hotel. I'm not sure I would do this if an airport change were not involved, but if you have to move around anyway I would rather have the evening in London.

As Janis suggested, last time I used priceline and got the Thistle Marble Arch for $72/night including taxes. The next morning I taxi'd to Paddington Station then took the train to LHR.

Am I able to charge tickets on National Express?

"Am I able to charge tickets on National Express?"

You mean pay by a card? Yes, but in that case you must buy the ticket at the ticket office (at the bus station at Heathrow T1-3; inside the terminal at Gatwick and Heathrow T5) before you board. Also, if you're planning to use anything other than Visa or Mastecard, check on the bus company's site whether they accept other cards.

You can also use cash to buy the ticket

Do you think they will take Euros or US dollars or are pounds needed?

GBP or CC please - but given recent rises in the fare it might be cheaper to pre-book a taxi service if there's more than two of you.

tidy, You could find out the bus fare then get £ cash from an ATM at the airport, but in your situation a credit or debit card would probably be the most practical way to pay.

You might check out a car service called Just Airports. I think they do transfers from one airport to another but I'm not sure. They take credit cards but they give a discount for cash, £'s of course.