There's no problem with using a possessive with an inanimate object. Both "bot's reply" and "reply from a bot" are okay. An alternative example would be something like "the room's furniture", "the tree's apples", or "the candle's light" to name a few.

The website's autoresponder objected with strong language. :) The station's welcome banner had long since fallen. The chatbot's perfomance surprised all present. The boat's bow nudged the broadwalk.

Bot's reply is fine. They both are good. You can still use 's with inanimate objects, like "the bot's reply"