Hi
A solenoid is a heavy duty switch operated by pulling a metal slug into a coil. Are you applying the jump lead to the switch terminal or to the input to the coil? It would be unusual for the metal slug to be vibrating in and out of the solenoid to be caused by a solenoid fault. It is more likely to be a bad connection.
Connect one jump lead from the positive terminal of the battery to the input to the coil and another to the starter body from the negative terminal of the battery.
If it still buzzes then you can be sure you have a faulty solenoid. You didn't say which bike or starter you have so I am assuming that you have a Valeo D6RA7 fitted to airheads from 77 to 95. It is easy to replace the whole solenoid on the Valeo starter, but even a second hand one is rather pricey from Motorworks etc.
You could take the parts from any Valeo D6RAxx starter you find at a scrapyard. They were fitted to a lot of small renault and citroen cars in the mid 90s.
My recommendation would be to fit one of these.
http://www.woodauto.com/Component.aspx?Ref=SND12901 A bargain at £14.
Instructions on dissassembling the starter here.
http://www.largiader.com/tech/valeo/
Steve