How to get tighter code

I use an embedded terminal (Tilda) full time on my desktop, as I connect to my network of Ubuntu machines mainly thru SSH. I set up an update notification script that tells me update staus remotely, but it's kind o' clunky (I know my scripting skills are far from pro). Here's what I set up:

Create a folder ~/.updates.
Create script called updates as follows:

#!/bin/bash
# cat updates
# A script to print out update status in bash
#
sudo apt-get update > ~/.updates/updates.log
sudo apt-get -s dist-upgrade >> ~/.updates/updates.log
cat ~/.updates/updates.log | grep upgraded,

This does the job, but I'm sure it's far from optimal. Anyone have any suggestions on how to get it tightened up? This sort of thing is easy to do in some distros (Arch comes to mind), but Ubuntu is designed more for things like Update Manager and other graphical tools, so this was the best I could come up with so far. I want to be able to just get the line for available updates (for use in other scripts), not all the associated printout.