Is that just a random part of the game or did I do something to cause it?

you upset off some NPC along your travels and they hired the DB to "deal" with you...

There's the hired thugs that might come after you if you successfully steal from an NPC. They will have a letter on them naming the NPC in question.

And then there's the Dark Brotherhood assassins that lie in wait for the player. The UESP has this to say about it.

Well, the Brotherhood doesnt put the bounty on you, someone else does, Happened to me like 20 times now, they fail everytime, I wish the assasins would hit you when you sleep/Sneak up behind you, not charge head first into.

It's random. Somebody once said they got attacked by that assassin at the beginning of the game, when heading to Whiterun from Riverwood.

Yeah, its just a silly random world encounter. Totally stupid on Beths part to make DB attacks a random encounter. What idiot assassin is going to charge head on in the middle of the day on a path to take out their mark? Getting you while sleeping, at night, etc, would have been much more believable. And to top it off they are carrying a note that indicates they are DB! I thought they were supposed to be secretive?

Random...and happens more than once per playthrough. Screw you astrid revenge shall be mine!

This. Also, because it can happen very early in the game (I was like Level 2 and it was my third character and she had interacted with no NPCs except Lucan and Adrianne so hadn't done anything bad) it wasn't credible that there was someone in the game that had done the ritual to summon the DB. Nor had there been time for the DB to send someone after me and even if they had, for the assassin to find me and then, ya, why would he be standing in the middle of the road somewhere when I was randomly wandering and wasn't doing any particular thing? How could he know where I was, where I was going and have gotten there ahead of me? It was just so unbelievably and painfully stupid.

In theory, they're not supposed to fail ...

Question on Astrid - can I just go look for him and take him out? Or do I have to join in the DB quest line?

you have to initiate the DB questline, only then can you take "him" out.

It's a she....and you could try to take her out, but of course she's incredibly powerfull
Next time one of her assassins tries to kill you, take those DB-clothes, and infiltrate their HQ in disguise....might help getting close to Astrid.