Sometimes, other times not. Why would someone rated 2000 blitz even ask that?
Is a fianchettoed bishop a good move in modern times?
i guess the best answer could be " dephend where are the remaining pieces"..
A lot of opening include a fianchetto variation and some of them are quite strong. So fianchetto its a good option, but there also plenty of examples ther the bishop whould be best developed somewhere else.
Hard to say anything further if you dont specify the opening, what bishop ( King or Queen side) and what color are we talking about..
BTW, it surprises me a bit that someone with 2000+ elo make a question like that... 
Well I bring this up because I had a game not too long ago where Me and a friend were playing when I fianchettoed my bishop playing as white. and like after that decision he just ripped my defense apart and mated me in like 6 moves.
Well, one of the disadvantages is that the advanced pawn provides a target for your opponent to conduct a pawn attack which opens lines against your king. Also, if your bishop gets trades off, the squares of the same colour around your king get weak.
Haha, you have a nice rating for not being studied! Play some players around 2000 in blitz some time and you'll understand why they questioned you :)
Every good move also has drawbacks (unless it's a mating attack ;)
The castled position is no less weak but the pawn move does make a pawn break easier to achieve and if the fianchettoed bishop is traded off, then the color complex around the king is weakened.
All this danger means nothing if your opponent does not have an attacking position though. The good is that it puts the bishop on the longest diagonal, where it influences the center of course, and all this from a corner where it doesn't get in the way of your other pieces.
Top players don't sit at the board wondering about a finachetto, or base their opening prep around it. The fianchetto is a part of many main line openings like the king's indian defense, king's indian attack, sicilian dragon, nimzo indian and queens indian defenses, the catalan, the english, etc.
These are all world class openings. What makes it a good or bad move is just like any other move, it depends on the specific position. In the opening it's a perfectly acceptable move. You can even go for it right away with your first 2 moves without much trouble... but if you can't generate play elsewhere, and you ignore an opponent's attack, then you may find yourself getting blown off the board (but actually this is true for any position).
I think like any strategy it has pros and cons.
The Sicilian dragon is a good example. The bishop is a great attacking piece, but there is a system (Yugoslav attack) based on exploiting the fact that the g pawn has been advanced but pushing up the h pawn and opening the h file against the king.
Ok so it's more or less one of those moves that has to be timed correctly and with the right move set to be effective.
Maybe not even that restrictive though. You can play it as your first two moves as white or black if you like, and it would be a legitimate opening. Here are some games of Kasparovs.
Ok so it's more or less one of those moves that has to be timed correctly and with the right move set to be effective.
As is true of all other moves really.
Im still missing the piece here. I usually don't fianchetto and things seem to work out fine and the few times I did fianchetto things got ugly.
Yes, of course 1 move can't make your position good or bad by itself. It always depends on the entire board... all your pieces and all your opponent's pieces.
I don't think anyone enjoys every type of opening. Everyone has a preference for the types of positions they play. It brings them good results, or they're more comfortable, etc. So if you never play a financhetto then that's fine too 
Is it a good idea to fianchetto a bishop? even with the pawn initial double move?