In all the years the Sorting Hat had lived, it had never seen a creature so magnificent. Now, don't get it wrong, the Sorting Hat has seen Dobby's kind around Hogwarts, particularly in the kitchen. But Dobby wasn't like them, no. Dobby was a free elf. And something about that made the Sorting Hat feel happy.
If you were to ask when they first met, they'd have different answers.
The Sorting Hat would say it was when Lucius Malfoy went to see Headmaster Dumbledore. At one particular time, he called Dobby. Although it was sure that Dobby didn't remember that time. But it was love at first sight for it.
Dobby would say they first met when Dobby had gone to warn The Harry Potter in Hogwarts.
They'd had little meetings when they met each other. No one knew, of course. But between those meetings, something had blossomed between them. The humans didn't know, they didn't want to tell them yet. But perhaps anyone who would see them together in a room would assume that there was something between them... Or perhaps not, as a sentient object and a slave elf would be a particularly weird match for them.
But maybe because of that, or maybe because of the thrill of sneaking around without anyone knowing, they never told anybody. And they never will.