The Baytril tastes really nasty and bitter. You mentioned in your other thread that she is now not eating, or it could have been put in a tiny amount of strong tasting food. My vet said they won't eat the food if you put it in, but Vectis recommended a particular brand of meaty dog food to disguise it (it is a safe one for hamsters) and that has worked for me.
However if she is not eating then you could try SKB's suggestion which is to draw a little bit of runny honey into the syringe after drawing up the baytril, so it tastes sweet and disguises the taste. But the only way to syringe feed it would be to hold her and insert the syringe into the side of her mouth. Did you see Vectis link on how to medicate hamster? It has some photos.
There is no way our robo likes being picked up at all and he also hates the syringe so I used the dog food method.
However, this medicine is life saving for your hamster so it seems the only option will be to hold her - swaddled in a cloth or blanket and held upside down, and put the syringe into the side of her mouth and insert the contents slowly, so she doesn't choke on it - hold her upright when it goes in - with the honey as well.
https://vectishams.webs.com/givingmedication.htm