The 'Real Time' host has little reason to be worried because a rep for HBO says Bill is fully vaccinated, and he's feeling fine. The rep says, "Bill tested positive during weekly staff PCR testing for COVID" but says he's totally asymptomatic.

Remember, the COVID vaccines don't guarantee you won't get infected, but are highly effective in shielding you from serious illness and hospitalization. Bill's a perfect example of that.

HBO says no other staff or crew members have tested positive for the virus and Friday's show will be rescheduled for a later date ... the network says they've taken all COVID safety measures seriously.

Bill's guests this week were supposed to be Neil deGrasse Tyson, "World War Z" author Max Brooks and "Hardcore History" podcast host Dan Carlin.