I wonder though, lead was used in paint, and many other things, for over 1000 years before it was discovered that it was harmful, I think most of the lead exposure for people, is when lead was used as an additive in gasoline, where cars turned it into a fine particulate matter, and as cars got more and more popular car pollution got more and more and it reached a tipping point and started to do real harm. If the bicycle was white, there may be lead in the paint, if it's a light colour, there is probably a lot less, if it's a dark colour, probably none at all, even if the paint is quite old.

If your concerned, then you want to contain it, as much as you can, wear a respirator and either a disposable painters suit or old clothes you can toss and gloves, work over a plastic drop cloth, put the clothes or the suit in it, wrap it up to contain any particles, and seal it up, and put it with the hazardous stuff for the annual hazardous waste pickup, or take it to the hazardous waste place for disposal. Call your city or town to know when this is....

I remember as a kid, pushing a drop of mercury around the desk in science class, now if you break a light bulb that contains 1/1000th the amount in it, it's the end of the world. I think a lot of this stuff is blown out of proportion these days.