Making a finite automata
Here is your suggested automaton, if I understand your transitions correctly (initial state is 1)



This automaton will only accept $\epsilon$, and words consisting of a number of $b$'s

Hints to make one that accepts your language:

Make sure that it accepts $\epsilon, a, b$ and make sure that you "move away" from accepting states when seeing a $b$ after an $a$ (keep in mind that $aabb$ is also a string in the language, i.e the second $b$ should make the machine go to an accepting state).