With the Roku Stick, you must have the factory remote to connect to a network. They don't support IR, so no generic remote will work. And at a hotel the phone app won't work either, because hotel networks have a security setting that blocks all connected devices from seeing each other. The app does not use BT. It uses the same network connection that the Roku does, so they must both be on the same private network that does not have any security blocks in place.
Considering what a new remote would cost, you might instead consider simply buying a new Roku. You didn't state what model Stick you have, but if it's the older purple stick (3500) you can't even get a replacement remote, so it's unusable without one. But if it's a newer Stick, you could probably get a replacement at a Best Buy store, or many other stores that sell Roku devices.
Dan
Roku Community Streaming Expert
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