Going just by a cold reading of the novel, here’s what I remember about what happened and what was said.
Lucy was turning into a vampire because Dracula kept snacking on her. Van Helsing didn’t worry about the kids being bitten by her, the “bloofer lady”, because he knew it was Lucy doing it and knew they were on their way to kill her. He also says that with her death, the kids, who have been tainted with the vampire’s touch, will return to normal.
As for Mina, she was never bitten, but was scarred by the Count on her forehead, and forced to drink his blood. She did almost turn into a vampire, having begun refusing food from Van Helsing when the six split up to chase down the Count, and being kept in check in the Holy Circle, and also her telepathic link to Dracula. Van Helsing speculated even that as the heroes grew closer, Dracula tried to sever his link to Mina, so that they may not use her to track him down. Indeed, she became less and less susceptible to the hypnosis, but whether that is due to her growing vampirism or the Count severing his link is not clear. She still was able to report back his travels in his wooden box on the water, so I don’t know what to make of it.
We don’t know what happened to the sailors on the Demeter, nor the children bitten by Dracula’s brides back in Transylvania, so that’s about all we can go by. But I do remember Van Helsing mentioning that anyone bitten by the vampire will become one upon death, unless that vampire who bit them was destroyed. I wish I knew what chapter it was, but seeing as how he’s as much of an expert as we’re to have on the subject, I would tend to trust that conclusion.
As far as I remember from the book, there wasn’t a clause that one had to be bitten repeatedly. I conjecture that Lucy was simply bitten repeatedly so that the Count doesn’t draw undue suspicion on himself, and to keep her alive for repeated feedings. The sailors, probably something about the vampire’s inability to travel across water made them inconsequential. We know he has no compunction as to creating new vampires due to his harem, I am willing to simply accept that it was a sexier story that Stoker was going for, therefore no male vampires except Dracula himself appears. I don’t think its beyond his power, at the very least
Still maybe he had to destroy the sailors on the ship, for the Count escaped in the form of a dog at its landing at the pier. Neither Lucy nor the Count’s brides showed any power to transform (except the brides swirls as mists before and after appearing), or to command beasts, so maybe creating a ship full of baby vampires would have undone his plan from the beginning.
I think, and I will believe this until disproven, that there has to be multiple ways to create a vampire, as supported by the Count’s change himself as he was never bitten. If simply the taint of a vampire is enough as Van Helsing surmises, then perhaps the bite is simply the easiest and most popular way, but that the Count knows he can get that disease into a person through forced suckling at his wounds as well, but that obviously is unknown to humans, so therefore he had the command of Mina for the longest time without suspicion by doing it that way.