Zoom in. 200%, 400%, 800%... what have you. The handles get bigger. Then you can tweak them and zoom out again.
Thanks, but I remember there was a setting to make them bigger?
That IS the setting to make them bigger. If they're really close to the keyframe, it means there's not much of a curve in the Bezier path at all. Once you can grab a Bezier handle, you just pull on it and change the path.... and if you don't want to change the path, there isn't much need to grab a Bezier handle.