Well... I would humbly suggest you work on the lunging...that's just plain rude!!
Get your little beauty to focus on you whenever temptation arises by carrying treats (her absolute out of this world to die for treats...IOW...a treat that is worth more to her than chasing a bunny..) and asking her to "watch me" BEFORE BEFORE she focuses on lagomorphs and rodents.... and when she locks eyes with you... TREAT! You gotta watch for that moment when the head stiffens, the ears are full mast...and get her before that happens.

I would also teach a "Leave it" ...Pat Miller's book describes a great way...and these work.

Of course NO dog in the world is 100% ---these are dogs after all---not robots, but you'd be surprised how much this will help.

I ride with my 60lb collie on my aluminum Globe....and I use the . SHe's not a lunger but when she would pull to the side or turn around (tempted by the world and all its glory) I would barely feel it. Let's go. I tell her and keep moving.

As long as you keep pedaling she won't pull you off. But I think a little off the bike work on lunging would be a good idea....I walked dog and bike together at first.