You have to be very careful not to asperate her. If you do not feel comfortable shoving the syringe down her throat then by all means do not. You can easily puncture of stretch her crop which could have fatal results. If you are more comfortable doing the dribble... then I say dribble away. Just remember to go with the syringe in your right hand to the right side of the birds mouth (the left side is the airway). I have never heard of a bird having hiccups. She could be bouncing because she is still hungry. I would not be able to say without seeing her. How old is she? How many feedings a day? Is she starting to eat regular food on her own?
Edited to add video: Here is a video from you tube I found that might help:
YouTube - How To Hand Feed Birds