Individual government figures tend to "pay their own way"... in a manner of speaking. If they can pass it off as a "fact-finding mission", then they bill it to the government.
Sometimes lobbyist organizations pay, but that falls into the government rules on "gifts", "campaign contributions", etc.
Usually, however, the government foots the bill for members/employees of the government, feeling it is better that the taxpayers as a whole pay for the trip, than for "undue influence" to be thrown around.