Honey, it completely depends on the person. It took me to learn it in 9 days (5 practices) to learn it. If you are at the stage, and you have the skills in order for it to work, you'll get it in no time! :)
The actual action of doing a back handspring only takes about 4 seconds. But, if you mean learning to do a back handspring, that time can vary depending on the person and the time spent practicing....
With the right trainer and the right equipment, it only takes about seven and a half hours of hard work and conditioning. Push ups will definitely help.