With Kalista's Black Spear, a binding can only be made within the first three minutes. With a binding you're pretty much dedicating yourself to the person you're oathsworn to, as you're expected to be paired for the rest of the game. It's not a glitch or a bug. If you miss the opportunity, that's it.The player can re-buy the spear at the shop in the first three minutes of the early game to ensure that in case there was a wrong binding at start game or if the player forgot while they were buying items they can still bind. But after the three minutes, it's just tough luck.
EDIT: As a response to the comment to my question, I'll further the answer more.
You can re-buy The Black Spear, but it's un-usable after a certain time frame. I've experienced this myself multiple times when I've had people quit. In fact I've done what the OP has done, and it's the same thing. When Kalista is bound to someone, they stay bound with her. It's how her game mechanic is supposed to work. If twenty minutes pass and the person Kalista is bound to AFKs/Quits/Disconnects, you cannot rebind, even if you have a new Black Spear. I'll also say that this effect does indeed happen if you forget to bind your partner. I learned a very harsh lesson very quickly when I discovered that I couldn't bind after 10 minutes into a game. You do have a time limit in which to bind your partner.