Well, of course, eye drops will give you a bad taste in your mouth. As we know that because of the different uses, there are different kinds of eye drops. In common, they have different chemicals which mix together. So when you get them in your mouths, it will taste bad. And you are not supposed to get them in your mouth. By the way, by using eye drops, it is also possible to get some side effects. For example, headache, dry mouth, eye discomfort may occur.
Yes, I have this experience. When I use the eye drops, I taste something in my mouth because the eye nerves and throat nerves are interlinked. It is normal to taste the smell when you use the eye drops. You jus use the suitable amount of the eye drops which could avoid such thing. You could also drink some water to make the taste become light in the mouth.
Ok, I can see you are quite puzzled here and worry about your health. But it is normal for you to have such experience of getting bitter taste in your mouth. Because your eyes and your mouth are connected to each other, sometimes tears would flow to your mouth, so does eye drop. Anyway, the eye drops are quite bitter sometimes so you can take it easy, there is no problem. Just try to protect your eyes as much as possible.