i am left with option to use the 3.3 V pin of the Arduino.
No you are not. A dedicated 3.3v HC-06 module exists but most Arduinos have insufficient power available @ 3.3v to use it. All bare HC-0x boards are 3.3v, but the same obviously applies, and probably require you to come to terms with using a soldering iron anyway.
This all seems pretty silly, but maybe you could use VIN or the ICSP cluster for alternative power. Failing that, you could invest $1 in a breadboard, which is what most people do at a time like this.