I will try help here. I like Zubats lol :3
So basically, you really need more moves on this lil guy :) Three moves isn't enough, so try level him up until he learns better moves. Leech Life is good, Astonish is mediocre, and Supersonic I s okay. Train Zubat up a bit more, and it learns Bite. It's not great, but it's a good fourth move. After that it learns Wing Attack at Level 21.
At Level 22, Zubat will try to evolve. I wouldn't say no, as the next best move it gets is Poison Fang, which is a very good move, but I wouldn't be able to bear having a Zubat until Level 41 lol. Evolve it, as Golbat has better stats, meaning it can take more hits and deal more damage. While you won't be able to evolve it again into Crobat until you get the National Dex, Golbat is, in my opinion, worth having.
3. Other Options
As others have said, even Golbat is not the best Pokemon. Other alternatives for a Flying type on the team would be Spearow/Fearow, or Pidgey/Pidgeotto/Pidgeott. Other notable Poison types are Nidoqueen, Nidoking, Beedrill, Vileplume, and Gengar.
Hope I helped!! Good luck with Zubat, too! :D