Asparagus spears always turn into a fern-like bush if they aren't picked soon enough. How many years ago did you plant your Asparagus? That helps determine how long your picking season should be. The first 2 years you aren't supposed to pick at all and should just let it fern-out. During Year 3 you can pick spears for about 3-4 weeks and then let them fern-out. During Year 4 you can pick spears for 6-8 weeks and then let them fern-out.
Also, what do you mean your asparagus "sprouted without you doing anything"? I have had asparagus my whole life and it has always sprouted without me doing anything. It is a perennial and comes back year after year on its own.
Maybe that is why I have never really gotten much out of it yet. It grows but it goes to bushy before it goes to spears. I've only had it two years so maybe this year it will grow again.