How long (time) it takes to go from Mumai dadar terminal to Pune city by road by bus or by cab ?

three hours

www.maharashtratourism.com

should not take more than 2.5 to 3.5 hours by taxi or a bus.

but beware off the traffic jams exiting bombay and once you enter pune.

take a private cab much quicker and takes you to doorstep .

travel time depending what time of day / night .
daytime == apx 4 hrs
night time == apx 2.5 hrs

also depends on the drivers car / knowledge.

i always use private cab

By road by bus it takes approximate 4 hours of course depends upon the day or night time. In late night there is no much traffic so takes 3 hours. By cab it takes less time in night time or early morning before 7 am. It takes just 2 hours to reach Pune by express way. It also depends upon the final destination in Pune. Aundh area is much closer to expressway while camp, Vimannagar etc are far away so takes half an hour more in early morning or late night. Day time it may take 60 to 90 minutes more.

by any mean of transport it will take anywhere in betwwen 3 to 4 hrs n dependz on traffic flow within city

There are buses starting from close to Dadar terminus, you have to exit the terminus to the EAST side and ask around. There are also taxis, you can either share or take a full taxi. If you go by road, the amount of time taken to exit Mumbai is totally unpredictable. Once you hit the expressway, you should make good time. Entering Pune again will be dicey in terms of how much traffic you hit, and where in Pune you want to go, i.e. where you exit the highway. Say between midnight and 7 in the morning, getting out of Mumbai will be a breeze.
By road is theoretically faster than train, but only the expressway part. Getting in and out of the cities takes a lot of time. Depending on the time, you should also look at the trains from Dadar to Pune. The total journey time might be the same, depending on the train you take.
Some details about your actual starting point/ ultimate destination within Pune would've helped.

arround 2 hrs from dadar @ night