Can I run Bash scripts in FreeBSD without modifying them?

You can call your favorite shell with the script as a parameter.

bash ./script.sh

I run FreeBSD myself. I found that starting the script with the following greatly improves cross OS compatibility:

#!/usr/bin/env bash

You asked to correct you when you were wrong. I'll try:

• Linux scripts are written in bash: Well, some are written for bash, others for dash and hopefully a lot potable for any POSIX-compliant shell.
• Bash script usually #!/bin/sh If they rely on non-standard bash features, it is highly recommended to have a #!/bin/bash shebang
• In GNU/Linux, /bin/sh is Bash That depends on the distribution. It can also be dash or mksh on Debian for instance.
• In FreeBSD, /bin/sh is not bash, it's the true sh. There is a lot of sh implementations. Which one is "true"? On FreeBSD, sh is based on the Almquist shell like dash or NetBSD sh. On OpenBSD, it's based on pdksh, on many commercial Unices, it's based on ksh88 (which is the basis for the Unix/POSIX sh specification). Some ksh88-based shells and bash are the only two shells that have been certified as being a Unix compliant sh implementation (when built with the right flags and in when in the right environment).

If you have scripts with /bin/sh shebang and want them to be executed by zsh you can try passing the script to zsh, but this will fail as soon as this script calls another script (and you don't want to modify it).

So I only see the possibility to have a symbolic link from /bin/sh to your zsh. But I don't recommend to do this, as it may have drastic impact on your boot time and will not even help you for some of your linux scripts.