Hader said they start filming Season 4 in two months, so my guess would be the next season will be out next spring.
SPOILERS BELOW
Now that Barry has been caught, I can't wait to see where they go with it. While I doubt they can tie him to Janice's murder*, you have a dozen cops witness his attempted murder of her father, so that alone is a charge that should stick. Barry often seems to magically get out of sticky situations thanks to sheer luck more often than not, but it will be interesting to see how they tackle this.
*In regards to this, I don't think he ever actually admitted it verbally to Gene, did he? When Gene asked him if she suffered, he lowered his head and shook his head to indicate she did not, but that is not an admission that would hold up in court. And if they had evidence to arrest him for that, there would have been no need for the sting where he was seconds away from actually killing Mr. Moss.