You can fly to Bagdogra from Mumbai ad then enter Bhutan by car through Phuentsoling. Or else fly from Mumbai to Delhi/Kolkata and then fly from Delhi/Kolkata to Paro.
You can either fly from Mumbai to Bagdogra airport and from there it will take you 4hrs to reach border..or u can also fly from Mumbai to Delhi and you can catch Delhi to Paro flight..but you will have to match the flight timing