How to use AppleScript in a bash script to create an alias for an app?

osascript will run AppleScript code in your shell. This example uses a HEREDOC to present the code to osascript.

/usr/bin/osascript <<'EOF'
tell application "Finder"
    set myapp to POSIX file "/Applications/Chess.app" as alias
    make new alias to myapp at Desktop
    set name of result to "Chess.app"
end tell
EOF

Source- Link

Why not skip the Applescript and just create a symbolic link in bash? It behaves exactly like an alias on the desktop except now you can work with it in bash. See this answer for a breakdown of aliases, hard links and sym links.

So, your command would be:

ln -s /path/to/application/MyApp.app /Users/username/Desktop/MyApp

Where MyApp.app and username is the name of the application and the user respectively.