Bass, a career foreign service official since 1988, needs to be confirmed by the United States Senate before he can take up the new assignment.
Born and raised in upstate New York, Bass previously served as the US envoy to Georgia.
This is Trump's first nomination for a South Asian country. He has yet to nominate his envoys for India and Pakistan, the two crucial South Asian countries.
The announcement came hours after Trump, along with Vice President Mike Pence, drove down to Pentagon to hold policy discussion with his national security and military advisers on a host of global issues including Afghanistan, North Korea and ISIS.
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At her daily news conference, White House Deputy Press Secretary Sarah Sanders reiterated that a decision on troop level would be taken by the Defence Secretary James Mattis.
"He (Trump) has empowered Secretary Mattis in terms -- I've been asked specifically about troop levels and decisions on specific instances, and in that regard, I would refer you to the Department of Defence," Sanders told reporters after Trump returned from Pentagon.
"Six months into this administration, there is still no new strategy for victory in Afghanistan either. It is now mid-July, when the administration promised to deliver that strategy to Congress, and we are still waiting," McCain said in a statement issued from the hospital in Arizona where he is being treated after being diagnosed with brain cancer.
A day earlier, the House Appropriations Committee passed by voice vote the annual Appropriations budget for the State Department. Among recommendation includes conditions on assistance for transparency, accountability, and other requirements, including prohibiting funds for new major infrastructure projects.
Within this amount, OCO funding totals USD 12 billion, which supports operations and assistance in areas of conflict, such as Iraq, Afghanistan, and Pakistan.