Apart from everything else, she is also an alien, she has alien technology on her side, she could have manipulated things around her to ensure her safety and good time, perhaps even do a trick or two to humiliate some of the racists she encountered, which might have impressed Clemens. Or maybe it's the other way round, and finding a decent human like Clemens was what helped her get the safety and the good time.
As an alien and knowledge, she had plenty of options, unlike some of the humans who lived there back then.
And in spite of the times the events took place, not all the while folks were racist assholes, and even many racist assholes are often willing to accept artists of any background. Could happen. It has happened. It's not the best thing to show, cause it makes you forget what the times were like, but it's also worth showing because like most times in human history, the world and the people and the culture are more diverse than you can paint it in a history book or a single story.
P.S. No, Picard didn't have to wait any time, him sending Data a message is something that had always happened, he left the message in the past, left it there, then was pulled from the past thanks to the future getting it. History was not changed.