Bush put us in Afghanistan and Iraq only, Syria was Obama's doing. So you're partially right there. Obama was in office for 8 years, promised on the campaign trail to pull us out of Afghanistan and Iraq, and yet.. we are still there. If he'd wanted to end our involvement in those wars, it was well within his power. Most of our allies pulled out during his term, yet there we remain.
And as far as "Bush put us in this middle east war".. We were attacked, and thousands of americans died. EVERYONE wanted war. You might not have been born or too young to remember, but the country as a whole wanted blood.
https://en.wikipedia.org/wiki/Authorization_for_Use_of_Military_Force_Against_Terrorists
Only ONE rep in the ENTIRE CONGRESS voted against it.
Afghanistan was not Bush's war, it was America's war. It is just one we no longer need to continue to fight. Iraq was horseshit from the start, and Bush can own that one. But of the three middle-eastern wars.. only one is republican owned.
Oh, and don't forget Obama's little "intervention" in Libya. At least that one didn't last, though.