I can add something to @st2000's excellent answer (in a better format than our discussion in the comments there).
The original question is vague. Does Bluetooth mean Classic or is Low Energy (BLE) acceptable or preferred. Which smartphones must be supported? Apple and/or Android? And what minimum version must be supported?
The 2.5 years that have passed since this question was asked makes it easier to choose BLE because adoption is so prevalent now.
I've been researching what it would take to implement a media control device as described in the original post. My target smartphone is Android Nougat. My goal is to skip podcast commercials. I have tested using a Bluetooth Classic keyboard. The media control buttons, Play/Pause, skip forward, skip back, etc. seem to do what I need.
I'd prefer to use BLE's support for keyboards and other Human Interface Devices: HID over Gatt Profile (HOGP). The KitKat release notes say that's when HID over GATT support was added, so it's been around for a while.
Having decided on a Bluetooth LE profile, device selection remains. Adafruit Bluefruit LE UART Friend has a HIDKeyboard example. I prefer an MCU with integrated BLE support. While total overkill for this application, I have an ESP32 that I plan to use for this. It has good community support and is cheap. If battery life (or size) becomes a problem, I'll look for a lesser device.