Baytril comes in different strengths so can not commend on the dosage. If the Vet has described by mouth, it is useless giving it in the drinking water. Budgies drink VERY little so would be lucky to get 0.001ml of the medicine. If it is not water soluble it will have sunk to the bottom of the water so he will get nothing. If it tastes foul... a budgie can easily go without water for 5 or 6 days so he might not be drinking at all.
Are you sure you are giving the correct dosage? 0.1ml is 2 drops so hold the bird in a hanky with one edge over its head/eyes so it can not see. Firmly grip the head between the thumb and index finger and have the body laying in the palm of your hand and close the other three fingers, you then have complete control of the bird. Get someone to carefully prise the beak open with a matchstick and squirt one drop on the tongue and let him swallow that, then repeat one more. It is easier to prise the beak open if you start at the side as there is a small gap there.
I am somewhat concerned at the dosage as overdosing on Baytril can cause the effects you decribed - although if the Vet gave you the medicine it was probably already diluted. Try waiting until evening for the first dose so there is food in the crop, and again one hour after light.
Good luck.