Recipient of a text DOES NOT get billed.
Just like calling a UK mobile that is abroad whilst in the UK does not cost more.
Unfortunately it is not quite that simple as some (all?) US carriers such as AT&T charge users to receive text messages.
- Sending a text to a UK mobile in the USA, then the cost would be taken from the senders inclusive minutes or charged at their normal text charge.
- Sending a text to a USA mobile would be charged at their operator's rate to text the USA plus the recipient may also have to pay to receive the text message. ( e.g. Orange phone to AT&T approx 58p = 40p (sender) + 18p ( receiver) )