He ordered Kreacher to leave without him
“And he order—Kreacher to leave—without him. And he told Kreacher—to
go home—and never to tell my Mistress—what he had done—but to destroy—
the first locket. And he drank—all the potion—and Kreacher swapped the
lockets—and watched . . . as Master Regulus . . . was dragged beneath
the water . . . and . . . “
—Harry Potter and the Deathly Hallows
Kreacher, of course, as a house-elf enslaved to the Black family, was bound to obey. Of course, he could have disobeyed his orders on pain of being compelled to punish himself in the future, but he seemed to have a great deal of respect for Regulus, and therefore would not likely have disobeyed.
As to why he specifically asked Kreacher to leave without him, we can only guess. The fact that he ordered Kreacher to leave without him suggests that he considered the possibility that Kreacher could leave with him. I can think of two possibilities:
- The potion would have eventually killed him. The potion may not have been immediately lethal, but it is possible that without drinking water immediately, the potion would be fatal. It seems unlikely he would have known this, though. If anything, Kreacher's example would suggest to him that the potion wasn't lethal.
- Perhaps he felt certain that Voldemort would hunt him down and kill him. He could never return to the Death Eaters, for fear that Voldemort would use Legilimancy to see what was in his mind. If he defected, Voldemort would kill him quickly anyway. Perhaps he preferred an immediate death to being hunted down by Voldemort.
Ultimately, neither of these explanations is entirely satisfactory. The second makes more sense, but requires Regulus to be fairly resigned or suicidal.
As an answer to your second question:
Bringing water probably wouldn't have worked
Harry tried to conjure water after Dumbledore drank the potion, but he failed:
Aguamenti!” he shouted, jabbing the goblet with his wand. The goblet
filled with clear water; Harry dropped to his knees beside Dumbledore,
raised his head, and brought the glass to his lips — but it was empty.
Dumbledore groaned and began to pant.
“But I had some — wait —
Aguamenti!” said Harry again, pointing his wand at the goblet. Once
more, for a second, clear water gleamed within it, but as he
approached Dumbledore’s mouth, the water vanished again.
trying, I’m trying!” said Harry desperately, but he did not think that
Dumbledore could hear him; he had rolled onto his side and was drawing
great, rattling breaths that sounded agonizing. “Aguamenti — Aguamenti
The goblet filled and emptied once more. And now
Dumbledore’s breathing was fading. His brain whirling in panic, Harry
knew, instinctively, the only way left to get water, because Voldemort
had planned it so...
—Harry Potter and the Half-Blood Prince
Clearly Voldemort had made plans, in order to leave a potential intruder with no other option than to drink from the lake and be dragged down by the Inferi. Presumably this would have extended to more mundane attempts to bring water into the cave, or to drink water therein.