Bilbo trusted that Thorin wouldn't let any harm come to him -- they had become far too close of friends for that. He trusted that if he overindulged in the ale, he would be safe and unharmed around Thorin. The dwarf could definitely hold more alcohol than Bilbo could.
"I know I am," he said, in response to Thorin's statement. He wouldn't have allowed himself to live in the same apartment as the dwarf if he didn't think as much.
Then, at that moment, his stomach grumbled rather audibly. Which caused Bilbo to look rather sheepish. He wasn't eating as much in Madison Valley as he would in the Shire -- though he was accustomed to fewer meals from the trip with the dwarves.