Is the private key static or variable key in the elgamal algorithm?
I never thought Alice and Bob would get international counterparts. Anyway, in reading your question I've spotted some issues.


Bashir generates a public and a private key. The private key you call a private session key, which is a bit confusing and may lead to errors like the one below.
In order for Amina to encrypt something for Bashir, she has to use Bashir's public key and also generate another value, (b), which is called the ephemeral key  or session key, hence the confusion I mention above.


To answer your question: Amina has to generate a new ephemeral key (b) for each message. If she uses the same key for all messages, and two messages happen to be the same, the corresponding ciphertexts will be the same as well. Moreover if someone gets his hands  on a plaintext, he can figure out the ephemeral key and seriously compromise all the messages encrypted with the same ephemeral key. Therefore Amina must generate a new ephemeral key every time.