Bluetooth auto connect to headset
Android surely can do that as well. Unfortunately, you've been a bit vague on the devices used: Samsung is a manufacturer having brought out plenty of smartphones, and there are also plenty of Bluetooth headsets; maybe there's something with that specific combination.

Nevertheless, there are some generic solutions available on the Playstore, like Bluetooth Auto Connect: It automatically tries to connect to your Bluetooth devices when Bluetooth has been turned on or when your device screen goes on. Unfortunately, this only works with Android 3.0+, so it's not really a solution for you – but a search for "bluetooth auto connect" will give you additional alternatives, one of those hopefully works with your Android version:

There's e.g. Shake To Connect working with Android 2.2+, which at least should save you from the "long walk through the menus".

Note however that I didn't try any of those solutions, so no guarantees :)