In a video clip posted on Wednesday on Bush's Facebook page, the former president, wearing a navy blue crewneck while sitting at a table, said he was challenged by his daughter Jenna Bush Hager to take the challenge, Xinhua reported.
"To you all that challenged me, I do not think it's presidential for me to be splashed with ice water so I'm simply going to write you a cheque," he teased viewers.
Bush: It's my privilege to challenge my friend Bill Clinton
As he wrote the cheque, Laura Bush appeared with a white bucket and dumped ice water over her husband's head and then said: "That cheque is for me. I don't want to ruin my hairstyle."
Bush then announced his nomination. "Now it's my privilege to challenge my friend Bill Clinton to the ALS Challenge."
The online campaign challenges people to either dump a bucket of ice water over their heads or donate to support research for amyotrophic lateral sclerosis, or Lou Gehrig's disease.
When a person accepts the ice bucket challenge, he or she must challenge another person to partake in the fundraising effort.
The campaign went viral throughout social media and has drawn a growing number of celebrities worldwide, includes Bill Gates, Stephen King, Christiano Ronaldo, and Lady Gaga, among others.