From Guns.com:

The 13-page Ammo Act would echo California’s background check requirement – under threat of a fine of up to $250,000 – but use the FBI’s National Instant Check System as a vetting database. To help fund the massive increase in checks, the bill authorizes $150 million in additional funds for NICS. This would eliminate home delivery in most cases, forcing those who buy ammo online to have it delivered to a local FFL for transfer, inevitably with a fee. Those completing a check would have to show a valid identification and include their name, address, and signature on a form devised by the U.S. Department of Justice. 

Further, the proposal would restrict what it deems to be “bulk ammunition sales” which it defines as “more than 100 rounds of .50 caliber ammunition or more than 1,000 rounds of any other caliber of ammunition in any period of five consecutive days.”