I've gotten caught a few times... in Solitude twice: emperor decoy, emperor's cousin's wedding.
Those are guaranteed detections, it's in the script.
Don't have followers. Some have morality settings that frown on murder (and DB contracts are still murder). Don't have a horse. Seriously, those things use telepathy to tell everyone what you are up to.
If you do use a bow, it's equally important that the target die before it detects you as well as your use of the bow goes undetected. Guards hear them. In fact, I've found that sneaking up behind the target and using my 1H sword is quick and quiet. I did that to a mark on the path between the Hag's Cure and the Hall of the Undead in Markarth. A guard sauntered up the path a half a minute later, but I had tossed the body in the river.
I agree, though that the best option, assuming your pickpocket skills are good enough (as well as the poison!) is the poisoner's perk. Twice I've had to kill a visiting noble in Dragonsreach. The first time he was seated alone to the left of the stairs leading up to the hearth. As I scuttled towards the door, he died, and that moment the guard said, "Ye gods!", unsheathed his sword, then put it away again. The second time, the noble was at the main table, a couple of chairs down from the head on the right side. Seated on the settle behind him was the Jarl! I crept up and planted the most powerful frenzy potion I had. Oh, lol, it's great when the mark gets himself killed!
And as was mentioned, you might try the "self-defense" method. No stealth, it's out in the open, and with luck you'll neither take any damage or have to deal any. This was the only option with one target in the main DB quest chain. He couldn't be poisoned (too high a level) and any sneak attack would be detected. But with the right choice of dialog, he was provoked, and the deed was done. Granted, General Tullius wondered why the guards let just anybody (me) into Castle Dour, but he let it go at that, lol.