You asked
So what would a BASSA member have to do, if they wanted to sign the contract on offer?
The answer is that an existing BASSA member is not able to sign the contract on offer. This is because you have delegated all power relating to negotiating your terms and conditions of employment to the union you joined. If the majority vote is for accepting the offer, then you can sign it, however, if your colleagues reject the offer, the only way you might be able to sign the contract would be to leave the union and gamble that BA would extend the period in which the offer is open. It might be something worth asking Bill Francis about. BA cannot induce you to leave the union