The RSA implementation that ships with Bouncy Castle only allows the encrypting of a single block of data. The RSA algorithm is not suited to streaming data and should not be used that way. In a situation like this you should encrypt the data using a randomly generated key and a symmetric cipher, after that you should encrypt the randomly generated key using RSA, and then send the encrypted data and the encrypted random key to the other end where they can reverse the process (ie. decrypt the random key using their RSA private key and then decrypt the data).
I can't use the workarond of using symmetric key. So, are there other implementations of RSA than Bouncy Castle?