Billy Bush is “horribly embarrassed” by the Donald Trump tape — while TV insiders are tittering that it must have been leaked by staffers on his former show “Access Hollywood.”

And while we’re told producers at “Today” and NBC News are appalled by his conversation with the presidential hopeful, Bush’s job at the morning show is safe.

An NBC insider said: “It happened 11 years ago … Billy was in a different place. He was a lot younger and more immature. He’s definitely embarrassed by this, but his job at ‘Today’ is safe.”

Another TV source continued, “Trump supporters might not care, but the ‘Today’ show will … they want Billy to look like ‘nice funny’ Billy, not a frat boy. The problem is that what to do if his interview subjects bring it up? He’ll have to address it on TV.”

Of his rival Matt Lauer, who isn’t happy about Bush being his heir apparent, the source added, “Somewhere in New York, Matt Lauer is having a big belly laugh.”

Bush told us in a statement, “Obviously I’m embarrassed and ashamed. It’s no excuse, but this happened 11 years ago — I was younger, less mature and acted foolishly in playing along. I’m very sorry.”

NBC was rife with conspiracy theories about how the tape was leaked to the Washington Post.

Another source told us: “There are only a few people who could have leaked this. The cameraman, who wouldn’t hold onto it. The editor, who also has no incentive to keep it and [‘Access Hollywood’ executive producer and close Bush pal] Rob Silverstein … They are the ones with access. There would be no reason to hold onto it from 2005. The only [reason to] leak it now [is] because of Donald Trump’s bid for president. NBC is in crisis mode. They have to protect [Billy].”

But Silverstein told Page Six when asked if he leaked the tape: “I am the last person in the world who would release that tape. Trust me. Let’s remember that. No chance. Don’t even infer it’s me. I don’t know who leaked it. I have no idea.”

Meanwhile, Bush and the “Today” show were both getting eviscerated on Facebook on Friday, with commenters flooding their most recent posts with nasty remarks. One user blasted “Today” for posting a story about “19 fall dinners that are pure comfort” in the midst of the Bush drama, snipping, “You can’t bury this story by posting a new article every 5 mins, it’s time to make a statement and take a stand against your employees behaving like 13 year old boys in a locker room.”

Warning: Explicit language