Is it just me anthropomorphizing, or do they seem to make little angry faces when you disturb them? I think it's cute, actually. Pet anger can be adorable when the situation is harmless. My cat makes angry faces all the time.
A betta bite is not bad.. it may startle you yes, but that was probably all it was.
I was bitten by my (at the time) 3 and 1/2 foot long silver arowana... I was cleaning the tank because everything was green and I didn't realize he was patiently waiting to pounce. I had both my arms in the tank and he got me near my elbow... boy did I scream and there was blood... That was the last time I stuck my hands in his tank and was a "lessons learned" to not wait 3 days before a water change and cleaning. LOL
My big red boy Hollow has bitten me and i mean held onto the skin but it didn't hurt. Their teeth are neither big enough nor jaw strength strong enough to cause pain. It feels like a very VERY light pressured pinch. You honestly only know it's a bite from the pressure because otherwise I wouldn't have known he was latched onto my finger xD. He did it when he first started feeling better and decided to get territorial with me, his thanks for saving his life. It's not that bad. And a betta is HARDLY strong enough to even pull your finger into the water. What are they like an ounce?