The above. 10" or longer. Thanks.

I haven't seen many bull barrels for the 22 LR in the last few years.  The trend seems to be to lighter AR-15's where the M-4 profile in rimfires.   DPMS sold two versions of heavy barrels.  I have a Gen I DPMS bull barrel and it is accurate.  The second generation DPMS use a bolt similar to a Ruger 10/22 bolt and report good accuracy.   CZ imported a dedicated 22 LR upper years ago which used a side charging handle and bull barrel.  I have been around three or four of these and all but one was very good and the other was just average.

For accuracy available today Compass Lake Engineering are expensive but accurate.  JP use a bolt similar to the Ruger 10/22 as does DPMS and Nordic.  JP are expensive but get good accuracy.  Byer barrels get good accuracy reviews as do Nordic.  Spike's used to sell Lothar Walther barrels which were accurate.

The CMMG barrels are rack grade and accuracy is very good on some barrels but others are not as good.   TACCOM barrels get good reviews but have been out of stock recently.

Accuracy Speaks used to sell a dedicated 22 rimfire upper but I don't know if they are still in production.  The CLE and AS were marketed as training rifles for DCM high power competitors.  Another company selling dedicated 22 rimfire uppers is Keystone.   I saw a review on one of their uppers which was positive but they are also pricey.

http://www.keystoneaccuracy.com/22lrmatchuppers.html

Vascar's answer is excellent and wide ranging.  I'll only add my one point of experience.

I have a 16.1 inch heavy taper.  As the name implies, it's heavy.  The accuracy is good, but not amazing.  With several sorts of inexpensive ammunition, mine will print five shot 1.5 inch groups reliably.  CCI minimag and Aguila subsonic can do better.  It won't outshoot a Kidd or Feddersen 10/22, but it is also more reliable than any of my 10/22s.  It's my current favorite.

I believe the chamber is pretty sloppy because it feeds the 45gr Winchesters my bentz chamber won't accept.  I believe it produced the accuracy it does because of the superiority of the AR barrel mounting system, and the weight and rigidity of the barrel.   It isn't really a bull barrel, but starts at just under an inch and tapers down to just over .85 inches.  It's a pig.

I have this bull upper from DPMS.  Very, very pleased.  thousands of rounds through it.  Fed 22 auto match absolutely never fails.  CCI minimag hollowpoints is close second.
Winchester copper plated hollow points not so good, but good for running FTF drills, LOL!

Excellent accuracy, always under .75" @ 50 yards, often under .50"  with the fed auto and CCI MMHP.  I'll blame that on ammo rather than the barrel.

DPMS current production 22lr AR bull