Is there any such thing as a "standard" Bluetooth remote?
Well, the device presents itself as bluetooth using the HID profile. That's a start.
Given that, I'd consider any remote that presents itself as a keyboard with well-defined keys to be extremely standard. (Remember, media control keys like "play/pause" and "fast forward" are well-defined and widely supported on keyboards already.)
Further, I'd consider any remote that presents itself as a gamepad with well-defined buttons to be extremely standard.
A remote that presented itself as a trackpad with standard buttons wouldn't be too bad either.
(I in fact often carry a bluetooth device that's remote-sized and is a full keyboard with integrated two-button trackpad and built-in laser pointer. It's hard to beat for presentations, and also controls my AppleTV and my Ouya very nicely.)
That said...if you want custom integration, Bluetooth is overkill. These things are implicitly already on the network. Just use IP.
That would currently require a bunch of one-off solutions, as there isn't a "standard wifi HID profile" to use. Myself, I'd rather have an app on my phone that presented itself to the world as a bluetooth keyboard or gamepad that I could then use even with devices that didn't have IP at all.