Is UART necessary to send AT-commands to Bluetooth module?
The module does require you to use the UART protocol in order to use it. It is possible to emulate a UART signal via bit banging, but this requires more from the MCU in order to make it work. AVR304 describes the most efficient way to do this.

Fortunately, the USI found in most tinyAVR devices, including the ATtinyX5, can be used as part of a half-duplex UART connection, alleviating some of the load. This is covered in AVR307.