One of the three airmen injured in the first attack, who were attached to 755th Expeditionary Security Forces Squadron, was evacuated from Bagram, according to reports.
The weekend bombings were the second time in as many months that insurgents inside the Kabul secure zone launched attacks against U.S. forces at Bagram.
In June, four airmen were killed in a mortar attack directed at the American air base, which, until recently, had not been a target for Taliban fighters in the area.
The fatal mortar attack occurred the same day as U.S. and NATO forces handed off the lead on combat operations to the Afghan security forces.
Saturday's bombings are only the latest instances of insurgents launching attacks against American and coalition forces deep inside the heavily fortified Kabul security zone in central Afghanistan.
Taliban forces have conducted roughly six high-profile attacks inside the security zone since early May, including a brazen daytime raid against Afghan President Hamid Karzai's compound in downtown Kabul.
Taliban fighters exchanged gunfire and rocket-propelled grenades with Afghan National Security Forces (ANSF) for over an hour as the insurgents attempted to breach the palace and the CIA's Afghan headquarters located within the same compound, according to recent reports.
Seven people were killed in the unsuccessful attack, but not before Taliban fighters disguised as ANSF soldiers were able to detonate a massive car bomb inside the presidential compound, according to news reports at the time.
Earlier this year, U.S. and coalition commanders warned that singular strikes on high-profile targets in Kabul would be the hallmark of this year's fighting season in Afghanistan, which will be the last for U.S. forces before the White House's 2014 withdrawal deadline.
These types of strikes at the power base of Afghanistan's central government will likely increase as the 2014 deadline for U.S. troops in country nears.
Foreign fighters are already streaming into the eastern part of the country to take on U.S. and allied forces for the final fighting season.
Pakistani-based terror groups like the Haqqani Network and others are calling upon “every house, every family” to send fighters into Afghanistan, Afghan army commanders stationed at the American base in Paktia province told The Hill.
The Obama administration plans to pull the final 32,000 American forces out of Afghanistan after the elections, officially ending the U.S. war in the country.