Another way, which is a little bit easier for me is to use named pipes. Named pipes provided a way to synchronize and sending messages between different processes.
A.bash:
#!/bin/bash
msg="The Message"
echo $msg > A.pipe
B.bash:
#!/bin/bash
msg=`cat ./A.pipe`
echo "message from A : $msg"
Usage:
$ mkfifo A.pipe #You have to create it once
$ ./A.bash & ./B.bash # you have to run your scripts at the same time
B.bash will wait for message and as soon as A.bash sends the message, B.bash will continue its work.