For me the joy of those shooters comes from spamming the button like a madman, having only one ammo kinda killed that. It could be an interesting mechanic, it creates tension when you miss,  however, but it would need to be visually conveyed to the player like the ammo is a boomerang or overheating. With the current implementation, it looks more like a bug than a feature.

only having one bullet is really annoying, and the enemy skips around the screen somewhat which makes it really annoying as well

A pretty nice concept! 

One thing to note is firing another bullet destroys the original one which tends to feel not that great gameplay wise. Its pretty unnatural and brings people out of the experience. Also leads to the game being more precision based which tends to be difficult with a rapidly moving enemy.

Another thing is hitting the a button after you've already started starts the game again which should probably be locked the first time someone does it.

A possible start to some really interesting ideas, but it would be good to see some of them played out more.

PROS:

• Not sure if it was intentional, but bullet-hell / shoot-em-up on rails could be an interesting idea where the game was more about properly timing your shots to eliminate threats rather than dodging. Would be an interesting twist and you could totally play up the visuals to give the illusion of bullet hell while the player never actually moves on screen.
• The game holds to the limited palette well and does try to create an interesting scene even with limited art.

CRITIQUE:

• Don't know if you meant to implement player steering controls, but it felt really weird that the enemy ships could shoot back at me even though I wasn't able to actually move. I initially thought this was a possibly clever design to give the illusion of threat while never actually being hit by enemy projectiles and then one of them got lucky and hit me and it felt like a cheap shot.
• The attempt at mocking up a parallax background falls a little short with just alternating between two frames of star configurations. I'd say you could probably get away with the trick a lot better if there were at least a couple more frames to create a somewhat continuous animation with trackable motion of each star in the bunch.