How to immediately trap a signal to an interactive Bash shell?

I try to send a signal from one terminal A to another terminal B. Both run an interactive shell.

In terminal B, I trap signal SIGUSR1 like so :

$ trap 'source ~/mycommand' SIGUSR1

Now in terminal A I send a signal like so :

$ kill -SIGUSR1 pidOfB

Unfortunately, nothing happens in B. If I want to have my command executed, I need to switch to B and either input a new command or press enter.

How can I avoid this drawback and immediately execute my command instead ?

EDIT :

It's important to note that I want to interact directly with the interactive shell in terminal B from terminal A. For this reason, every solution where the trap command would be executed in a subshell would not work for me...

Also, terminal B must stay interactive.

Based on the answers and my numerous attempt to solve this, I don't think it's possible to catch a trap signal immediately in an interactive bash terminal.

For it to trigger, there must be an interaction from the user.

This is due to the readline program blocks until a newline is entered. And there is no way to stop this read.

My solution is to use dtach, a small program that emulate the detach feature of screen.

This program can run a fully interactive shell and features in its last version a way to communicate via a custom socket to this shell (or whatever program you launch)

To start a new dtach session running an interactive bash, in terminal B :

$ dtach -a /tmp/MySocket bash -i

Now from terminal A, we can send a message to the bash session in terminal B like so :

$ echo 'echo hello' | dtach -p /tmp/MySocket

In terminal B, we now see :

$ echo hello
hello

To expand on that if I now do in terminal A :

$ trap 'echo "cd $(pwd)" | dtach -p /tmp/MySocket' DEBUG

I'll have the directory of the two terminals synced

PS :I'd still like to know if there is a way to do this in pure bash