Bullywugs are petty, bad-tempered humanoid frogs, native to swampy areas. The fifth-edition Monster Manual flavor text describes them as “struck with a deep inferiority complex . . . desperately crav[ing] the fear and respect of outsiders” and says they’ll generally prefer to capture trespassers rather than kill them outright, hauling them back to win favor with their rulers first. One way they do this is by taming giant frogs and having them swallow victims whole; however, this works only on Small or Tiny targets, meaning that unless a party of player characters is made up entirely of halflings or gnomes, this isn’t a strategy they can rely on in a typical encounter.
For a creature with only two hit dice, bullywugs aren’t too shabby in combat. All their physical abilities are modestly above average; they have proficiency in Stealth and the Swamp Camouflage feature, which grants them advantage on Dexterity (Stealth) checks in swampy terrain. It’s fair to say, therefore, that bullywugs won’t venture outside such areas—not when they have such a natural advantage on their home turf.
Moreover, their Standing Leap ability lets them move their full speed of 20 feet per turn as a long jump, when the jumping rule would normally allow them to leap only 6 feet. This allows them to cover distance in difficult marshy terrain without having to halve their movement speed. If you want to be nitpicky about it, you can require them to succeed on a DC 10 Dexterity (Acrobatics) check when they land, per page 182 of the Player’s Handbook, but personally, I’d say that bullywugs, whose natural habitat is the swamp, shouldn’t have to make that check when landing. And for the sake of flavor, I like the idea of having bullywugs bouncing around like a bunch of ornery little superballs during combat rather than trudging around in 2-D as we landbound humanoids must. (Mind you, this does not exempt them from opportunity attacks when they jump out of PCs’ reach.)
OK, so far we’ve established that bullywug encounters will occur in swamps. Let’s also stipulate, based on the aforementioned features, that their favored strategy is ambush (their physical abilities don’t indicate a preference for one form of combat over another, but their features do). Now let’s add, based on their 40-foot swimming speed, that they prefer combat to take place near open water: this is their favored method of escape. From the bullywugs’ point of view, the ideal ambush location is on ground solid enough to fight on but also near water deep enough to swim in. They’re Medium creatures, so this depth will be at least 3 feet.
Wanting, ideally, to capture rather than kill, bullywugs will attack in numbers large enough to surround and overwhelm a party of adventurers—let’s say three to one. But here’s a question: If you can get a free attack by popping out of hiding and surprising your enemies, will you really forgo that attack and demand their surrender when it costs you the benefit of surprise if they decide to fight back? Bullywugs aren’t bright, but I think even they can grasp what the whole point of an ambush is. They’ll take that surprise attack, thank you, and with any luck, the damage they do in the surprise round will serve as further incentive to stand down.
So here’s what round 1 looks like: The bullywugs lie in wait, hidden, at a range of 15 to 20 feet from where they expect the PCs to pass. At the right moment, they spring out of hiding, land next to the PCs, and kick off melee combat with surprise, spearing and biting. In round 2, they’ll keep attacking while demanding the PCs’ surrender—in Bullywug, because they’re too dumb to realize that the PCs don’t speak Bullywug. In round 3, they’ll also keep attacking and demanding the PCs’ surrender, still in Bullywug but louder and more slowly. If any PC drops his or her weapon, the nearest bullywug will grab and grapple that PC and pull him or her away from the fight, rifling his or her pockets and pouches for anything valuable.
Bullywugs are essentially cowards. If one is moderately wounded (reduced to 7 hp or fewer), it will leap away, but it won’t flee just yet—it will look for an opportunity to get back in the fight alongside a couple of less-wounded allies, and in the meantime, it will stay hidden and reposition itself with Stealth. However, a seriously injured bullywug (reduced to 4 hp or fewer) will indeed flee, using the Dash action to double its movement speed, leaping into the nearest water deep enough to swim in (and possibly incurring one or more opportunity attacks), then swimming away. If no water of sufficient depth is near enough, it simply leaps twice, 20 feet each time. Bullywugs will also flee when their numbers are reduced to fewer than one-and-a-half the number of PCs, then attempt to regroup with other bullywugs in the area, stalk the PCs and attack again when the opportunity presents itself.