Being too lazy to use "have". It's not needed to express the meaning but it should be added in proper English. If you use "gotta" instead of "got to", then it's better to use "I've" instead of "I have" too. Regarding "I have got to go now" and "I have to go now", they are the same.

I gotta go now. <- slang

I gotta go now - an extremely informal expression, not strictly grammatical, but people do say or write it I have to go now - grammatically correct and neutral expression for speaking and writing