Bush's paperwork was filed at a time of great uncertainty among top Texas Republicans.
Rick Perry succeeded Bush's uncle as Texas governor in 2000 and has now held the job longer than anyone in history. Lt. Gov. David Dewhurst has been in his post for a decade. Both are eying re-election runs in 2014.
That's sparked a logjam among GOP statewide officeholders, many of whom are anxious to move up — and that was before Bush entered the fray.
Attorney General Greg Abbott has raised $14 million, presumably to run for governor. Patterson and Agriculture Commissioner Todd Staples have already said they will challenge Dewhurst, while Comptroller Susan Combs and state Sen. Dan Patrick are also expected to run for lieutenant governor.
As a newcomer, Bush will likely wait to see how the field settles before he announces what office he'll pursue.
If Perry decides not to seek another term as governor in 2014 — a possibility since he may want to run for president two years later — then Bush will likely want to run for attorney general. But if Abbott stays put, Bush is expected to run for land commissioner while Patterson campaigns for lieutenant governor.
Adding to the intrigue is the fact that Perry and the Bush family don't get along very well. Perry served as George W. Bush's lieutenant governor and once unsuccessfully sought a judicial appointment for his brother-in-law, whom Bush shunned.
Both sides claim the feud has long since cooled, but the Bush family made no secret of its support for Romney, even when Perry briefly challenged him for the Republican presidential nomination. And Jeb Bush has been mentioned as a possible presidential hopeful for 2016, which could pit him against Perry.
Patterson said he believes either attorney general or land commissioner is George P. Bush's likeliest potential destination. The land commissioner administers state-owned lands and mineral resources.
"He comes from pretty decent lineage of folks who've been successful in politics," Patterson said.
Meanwhile, all officeholders will keep an eye on Bush to see if he tries to follow in Ted Cruz's footsteps.
Instead of working his way up the Texas GOP ladder, Cruz ran for the U.S. Senate in his first election. He stunned Dewhurst in the Republican primary before being elected Tuesday as successor to retiring Sen. Kay Bailey Hutchison.