The reason why President Bush held the Saudi kings hand was in respect to the Kings age, nothing else.
Evidently, the Saudi king is suffering from some elderly related infirmities. The famous clip I saw of Bush “holding hands” with the king showed the king stumbling and bumbling like he was unsteady on his feet, so Bush took his hand and helped steady him as he walked. Now, the only part of the clip the left shows is the holding his hand part of it, not the stumbles of the king.