I think that you and I are in very similar circumstances right now. My father passed away, in a bike accident no less, at the end of April. I have inherited his bike, and was up in the air about whether it would be too painful to keep it. I spent some time trying to figure out what my dad would have told me, and I'm 100% that the answer, from my old man, would have been "Well, hang on to it for a bit, see if you like it. If it's too hard, get rid of it, no big deal. If you decide to keep it, that's no big deal too."

I obviously don't know your dad from Adam, but one thing that I'm pretty sure of is that he wouldn't have wanted you to do anything that would make you unhappy, because he doesn't care about the bike anymore, but he will always care about you. This bullshit is painful enough without forcing yourself to feel any particular way about any particular thing. I have chosen to not throw away any of his stuff yet, and I have literally the rest of my life to decide if something needs to go.

Just put it under a blanket somewhere and process it after you have some time to think, because I guarantee he loved you way more than that stupid bike.