What is causing email sent from my Google Apps account to bounce?

First add SPF record to your DNS zones

offby1.net.    IN      TXT "v=spf1 a mx include:aspmx.googlemail.com _spf.google.com ~all"

It basically says that google apps is sending email on behalf of offby1.net.

Also add this to your MX records (from a short inspection it seems you don't have all the MX records).

offby1.net.    14400   IN      MX      10      ASPMX.L.GOOGLE.COM.
offby1.net.    14400   IN      MX      20      ALT1.ASPMX.L.GOOGLE.COM.
offby1.net.    14400   IN      MX      20      ALT2.ASPMX.L.GOOGLE.COM.
offby1.net.    14400   IN      MX      30      ASPMX2.GOOGLEMAIL.COM.
offby1.net.    14400   IN      MX      30      ASPMX3.GOOGLEMAIL.COM.
offby1.net.    14400   IN      MX      30      ASPMX4.GOOGLEMAIL.COM.
offby1.net.    14400   IN      MX      30      ASPMX5.GOOGLEMAIL.COM.

Then I would go and search RBL database, and find out if your domain/IP has been blacklisted.

A quick check show that your domain is listed: http://www.mxtoolbox.com/SuperTool.aspx?action=blacklist%3aoffby1.net

It's possible that your IP is listed there because this IP isn't supposed to send mails (that usually happen with entire IP class of certain ISP or hosting companies, and you're required to send a request on that RBL to add that IP as an authorized IP to send email).

Hope it helped.

I would recommend changing your password - if your account has been hacked (and then flagged by Google as a possible spam source) they sometimes will bounce your outgoing email. Changing your password "should" clear the flag - at least it did the one time I had this problem on one of my accounts.