Did George Bush propose a law to ban same-sex marriage?

If you are referring to the senior George Bush, no.

If you are referring to the junior George Bush, the answer is still no.

The federal law banning federal recognition of same-sex marriage dates to 1996, during the Clinton administration, which occurred between the two Bush administrations.

During the junior Bush's presidency, there was a proposal to amend the constitution of the United States to ban same-sex marriage. This is a constitutional amendment, not a law. It was not proposed by President Bush. It was defeated in the legislature and never made it to Bush's desk for signature or veto.