Question: I just want to know whether both the usages are right or not. Also, do these usages depend on geography?

Answer: 
It's a noun so it's necessary to specify the quantity. "One hundred" is the same as saying "a hundred," just like if you had six hundred it would be necessary to say "six hundred." The same rule applies to other nouns; you don't say "I have dollar" you say "I have one dollar" and you don't say "I have car" you say "I have a car." (or, of course, "I have six cars").
'Hundred' is a noun, not a quantity. Thus it needs a determiner like 'a' or 'one' to function as a quantity. 'Dozen' is functionally similar.