best way is if you want a comfortable ride,take a cab. If you want to know real kerala as well along the way get on a bus.

April is not ideal time to visit. Base is not accessible by car

There has been severe damage to the entire region around the falls because of the recent heavy rains and floods and quite possibly the trekking path is lost. As of now the area is cordoned off and visitors are not allowed anywhere near the falls. It would be best to check just before the trip to see if the situation has improved though I am not sure it would be open by 1st week of Oct. In the normal course there is a reasonably navigable, though steep, footpath down to the base of the falls and you could carry your child down with you -- not pram-friendly. It is a normally safe area. You should allow three to four hours to go down, see the falls and come back. Please check on the status once again before your travel date. Enjoy your travel.

Currently In Southern India they are experiencing the full force of the Monsoon season, and it's close to the heaviest falls they have ever had. Kerala, Ernakulam and many surrounding areas are inundated. Some 31,000 people have been displaced, and are taking shelter. Despite the falls being 60 out of Kerala,there are many low laying areas on the way, and I imagine these would be in flood also.

Off course, Bike riding is allowed

I note the enquiry was 4 months ago. The season for visiting is between September and January and in this period bathing would be fine. There may be some restriction at the base of the falls as there are some safety issues. The rocks can be very slippery entering the water.