Cheapest, simplest way to implement a Bluetooth keyboard/mouse?
You'll find this is often the case, when you try to build something from off the shelf parts that duplicates an existing product, almost always the parts alone will cost more than the existing product. The reason being that they can mass produce their product, buying parts in bulk cuts down on costs etc.

Look closely at the 'serial-over-Bluetooth boards', some of them do in fact support different profiles. What you are looking for is a module that supports the Bluetooth HID profile (Human Interface Device, aka mouse, keyboard, joystick, wii remote, etc).

Check out this previous question, it lists several bluetooth modules, which you can buy in single quantities for fairly reasonable prices, some or all of them should support HID.