Will bitter gourds/ bitter melons/ ampalayas grow in hydroponics planting?

How long will it take compared to soil planting?

What is the best hydroponics method for this plant?

One of the hottest topics in hydroponics at the moment is the effect of beneficial bacteria and fungi on your final crop size and yield. A number of products are now coming onto the market to enable you to harness the natural benefits of beneficials.

In my experience as long as you are planting a rooted sproutling in the hydro system, and you have a big enough table to hold your gord as it is growing you'll do fine.
The time it takes will depend on th lighting situation you have set up with your hydro sysstem.
I have 1000W 12 on/12off and my system is excellent for growing anything.
I also use a 3 part fertilizer and be sure to clean system trays and all components with 1tsp bleach in 1qt water.