Can you please check with creating a user named "guest" in the DatabaseB. This will enables any user with an Adaptive Server account to access the database as a guest user. If a user who has not been added to the database as a user or an aliased user issues the use database_name command, Adaptive Server looks for a guest user. If there is one, the user is allowed to access the database, with the permissions of the guest user.
The database owner can use sp_adduser to add a guest entry to the sysusers table of the database:
sp_adduser guest
Please also verify that the suid is -1 for guest user as below :
select suid, name from sysusers
~Regards Gaurav