When dying in CoS to a boss, a text would appear in output or perhaps a button on the screen offering to take you back outside the boss room for a price. Might be expensive.
I'd probably only use it for the Fallen, if i ran out of teleport stones first. Don't mind walking to Bassy or the Stickman.
It'll probably cost a teleport stone though.
Oh. But you said it would be expensive :D
You die once.. then twice... and before you know it, you've died over 9000 times, bam no more teleport stones.