After much trial and error I frankensteined this code for my purposes from a apple script from Tom's answer to a somewhat similar question a couple years ago. It would be neat to have this run in the background without actually opening up the Menu but it's not of major importance.
use AppleScript version "2.4" -- Yosemite (10.10) or later
use scripting additions
tell application "System Events"
tell application process "Bear"
tell menu bar 1
tell menu bar item "Note"
try
with timeout of 0.1 seconds
perform action "AXPress"
end timeout
end try
end tell
end tell
end tell
end tell
do shell script "killall 'System Events'"
tell application "System Events"
tell application process "Bear"
tell menu bar 1
tell menu bar item "Note"
tell menu 1
tell menu item "Open In New Window"
perform action "AXPress"
end tell
end tell
end tell
end tell
set frontmost to true
end tell
end tell