Obviously you shouldn't travel at night, especially without companions, but if you have absolutely have to... Here's some tips.
Regarding avoiding bogeymen at night, I've noticed that they don't pop up when you're travelling in deserts, badlands and the like. Instead you might have to deal with trolls, bandits, animals, other night creatures and stuff but never bogeymen for some reason.
Never sleep outside at night. Sometimes they get the jump on you and get a few hits in while you're still unconscious. That really sucks. Plus, when you get up you may still be 'stunned' so that slows you down quite a bit. It helps your chances, even if only by a little, to stay awake.
If you want to outrun them, then the best thing to do if you can't get to a town before it turns dark is to get as close as possible, then run as fast as you can while trying not to get into a bogeyman's range. An adventurer with average speed can accomplish this with luck (i.e. the randomly-generated bogeymen aren't super-fast or strong) but it may take a long time before you actually get there because you can't use the travel screen. You can also use cleared-out monster lairs or caves.
Once you get strong, fast and skilled enough it's pretty easy to just slice bogeymen in half until they stop coming. Simply aim for the lower body. If you're not on the level to take them out in one hit, then I wouldn't recommend engaging them because they have a tendency to hit really hard. If you're confident, then you can jump around a bit and wait for them to come into range before you get into range of them (that's basic DF adventurer mode combat, really) and try to cripple them by lopping off limbs etc. before going in for the kill. Decapitation works best. Make sure they don't surround you; take them one at a time. It's best to aim for the extremities, i.e. hands and feet, because they are easier to hit. Also keep in mind that they can still die of blood loss. If you're using a blunt weapon then smash their bones up a bit, then stab in the face with a spare dagger or sword. If you don't have one, pulverise their faces. Patience is key, as always, when it comes to killing with blunt weapons.
Another good tip is to have the best equipment possible, but I guess that goes without saying. A good helm can be a lifesaver, and gauntlets and boots can prevent cripplingly painful bone damage. I've noticed, though, that for some reason armor works only half as well when you're asleep. Not sure if that's just my luck and the RNG likes spawning bogeymen with armor-piercing fists when I'm asleep, but I guess it probably has something to do with armor skill.