Script menu: how to reference user-path utilities (PATH / environment is missing) Summary
How can I execute scripts from the system-wide Script menu with a normal environment? It seems the environment is not being setup at all.
Scripts that are run from the script menu can find and execute commands from the base system. However, user-installed utilities are not found on the path. Also, /usr/bin/env foo is not finding commands that are installed outside of the base system.
Background
The system Script menu appears at the right side of the menu bar. It is enabled via Script Editor.app &gt; Preferences &gt; Show Script menu in menu bar. It displays scripts located in ~/Library/Scripts and other system locations. The menu can execute AppleScript, JXA, bash, python and other scripts (use shebang as needed).

Investigation So Far
Scripts that are run from the Script menu don't inherit the user's bash environment. They know the shell is BASH and your USER name, but no initialization occurs. I ran a little script to dump the env to a text file
~/Library/Scripts/dump_env.sh (be sure to make executable):
#!/bin/bash
env &gt; ~/env.txt
ps -ef &gt;&gt; ~/env.txt

Here are the interesting entries.
USER=mat
LOGNAME=mat
SHELL=/bin/bash
PATH=/usr/bin:/bin:/usr/sbin:/sbin
PWD=/
HOME=/Users/mat
_=/usr/bin/env

It is very vanilla. None of the custom paths are included. For example, the following are unavailable:
/usr/local/bin/svn # Subversion source control client
/opt/local/bin/python3 # python3 installed via MacPorts
~/bin

The latter two are normally sourced in my .bash_profile. /usr/local/bin/ is setup by path_helper which is called by /etc/profile (though apparently not for the Script menu).
I'm running macOS 10.13 High Sierra, but I'm interested whether others are getting different results.
Ideal Solution

Avoid hard-coding path to executables in shebang. Ex: if I install a different python version / distribution, I want to use it in all my scripts. /usr/bin/env python3 accomplishes this, but it seems to depend on the PATH?
Finds utilities in /usr/local/bin
Specify PATH once for CLI and Script menu (and GUI?). If I install a new Python I would like it to be used everywhere.
Specify PATH only for user-level processes. I don't want system processes using binaries from in my add-on path entries (especially user-permissioned path entries).
Avoid breaking 3rd party builds/installers/programs that were written with assumptions about what is present on my macOS install.

I'm looking into launchctl, which can be used to setup environment for GUI apps. Not sure if it still works or if it will work with the Script menu.
Update

I added trace statements to all of the bash environment files: /profile, /bashrc, ~/.bash_profile, ~/.bashrc. These statements export environment variable so I can see that the file has been sourced. None of these are getting run for scripts run from the Script menu.
launchctl setenv KEY VALUE will set an environmental variable for all processes subsequently launched by launch services (launchd) in the user space.
This works for Terminal.app, GUI applications and scripts that are double-clicked in the Finder. However, it does not work for the Script menu.
I added ps -ef to the dump_env.sh script. This tells me the Script menu is not invoking bash with any arguments that would strip the environment (such as -r or -p). The parent process is UserScriptService.
Running…
otool -tV /System/Library/Frameworks/Foundation.framework/Versions/C/XPCServices/com.apple.foundation.UserScriptService.xpc/Contents/MacOS/com.apple.foundation.UserScriptService.

…reveals a symbol named __NSUserScriptTaskServiceStart. This sounds awfully similar to NSUserScriptTask in the CoreFoundation API. From the API doc:

The NSUserScriptTask class is able to run all the scripts normally run by the one of its subclasses…

https://developer.apple.com/documentation/foundation/nsuserscripttask?language=objc
I strongly suspect this is what the Script menu uses to execute scripts. The API doc does says nothing about the script's runtime environment.
bash can startup in three different ways and how it uses rc files is different in each case.
To give a short answer when it is called as a login shell it reads .profile or .bash_profile to set things like PATH. When it is called as an interactive shell but not a login shell, say you run bash from the command line, then it reads ~/.bashrc to set these things.
If it's run from a shell script (or by launchctl) then it looks for an environment variable BASH_ENV and runs the file named in the variable.
Check https://www.gnu.org/software/bash/manual/html_node/Bash-Startup-Files.html
To answer your question you should set all variables in .bashrc, call that in your .bash_profile file with the line if [ -f ~/.bashrc ]; then source ~/.bashrc; fi Finally in .bashrc you should set the BASH_ENV variable export BASH_ENV='.bashrc'
This would then give you a PATH and so on everywhere.
When you move to the zsh shell things are slightly different, read http://zsh.sourceforge.net/Intro/intro_3.html
Most Mac admins and engineers ignore it all and we hard code the path to all our software in scripts. I've certainly never seen an Apple script that didn't have all the tool paths hard coded.