A rep for the actress tells us Alyssa reached out to Britney privately Wednesday to apologize after BS took to Instagram to slam a tweet of Alyssa's that she considered "bullying." As for how AM got the message across ... Brit sources tell us she sent a private message Britney's way this morning.

It's unclear if Britney reacted to Alyssa's apology, or what exactly Alyssa said in her message. We do know, however, that Alyssa expressed support for Britney in her correspondence.

ICYMI, Britney posted to her IG Story Tuesday, honing in on a tweet Alyssa fired off in December, which read ... "Someone please go check on Britney Spears." This is when she was off the radar and fans were concerned -- speculating she'd been re-conserved.

In response, Britney wrote ... "It saddens me to see things about me from people who don't know me!!! This definitely feels like a form of bullying!!!" She added, "Ladies, we are supposed to be rooting for one another not pulling one another down!!!"

Britney's been out in public since December, of course, but that outing didn't seem to go all that well ... at least from the outside looking in. Remember, we'd been told she appeared to be having a manic episode at a restaurant -- but both she and her husband denied it.