Typically eye problems like a scratch or infection are treated with topical meds (but there can be exceptions to this- pain meds for bad injury and or pain and swelling or severe infection). Topical meds are applied right to the source of the problem- so they tend to be pretty effective. And depending is causing the redness and discharge will determine the medicine used.
For example- I use antiobiotic drops with dexamethasone for my cats eyes- she sometimes has goopy eyes and redness and it has been determined that it is not an injury (she has had stain applied to her eyes a couple different times). And her eyes get better on the drops- so when her tear ducts get inflammed her natural tears cause a brown gook in the corner of her eyes. It is not harmful to her eyes, and the cause in her case is believed to be genetic- small tear ducts/not normally functioning tear ducts. If she has a scratch on her eye though- using these meds with the steroid (dex) would inhibit the healing of an injury or scratch and might cause scarring.
If they do put your bunny on eye meds be sure to as them to demo how to apply the first dose. It is pretty easy and I am sure most of us here can talk you thru it- but seeing it first hand can help a lot!
Julie