You can try these places. I order this for my boss during the summer months and sometimes they run out quickly so try and order as early as possible! I haven't purchased this in awhile so I can't guarantee they sell them any more. I think there are a few other places to order but I can't remember them.
1) Cafe Duke: 42nd & Broadway (but they may only have it during summer time)
2) Pergola: 39th btw 6th & Broadway (also have a great sashimi salad if you're into sushi)
3) New Star Deli: 7th Ave btw 39th & 40th
140 W 51st St, New York, NY 10020
where in times square are you?
k-town is just a stone's throw away so there are really quite a few options...
some of the places that i really like in k-town (albeit not necessarily for the bibimbop but generally speaking) are woo chon at 10 W 36th St and kum gang san at 49 W 32nd St.