I never had this problem with bikes, but I have been a bit of a hoarder when it comes to books and cooking equipment. One approach is to consider how often you use something. If you don't use a particular bike in one year, you could probably get along quite well without it. Or you might need a cutoff like "Used less than five times in the last year."
There's some good discussions of this on the Simple Living sticky thread, especially posts by @
Smallwheels and a few others.
Giving a bike away, or selling it at a fair price, may actually bring you more happiness than hanging onto something you barely use and don't really need. Not to mention the happiness it will bring to the recipient.