I received an email from Barbara Bullard telling me that my computer
is infested with adware and spyware and offering to clean it for free
and to sell me a software package, Ad Eliminator,which is "better than
Norton and symantec", for $ 29.95 if I respond by October 1.
Did anybody hear fom this Barbara Bullard or Ad Eliminator or is it a
come on to infect my computer with a virus?

Dear Vaac, 

As I explained regarding another question of yours, what you received
is an unsolicited mail, in the sense that someone sent you mail
without you asking to receive it. This is illegal practice in any
countries and considered immoral business practice, even when it is
not illegal. (SEE: Discount software
<http://answers.google.com/answers/threadview?id=362771>).

Now, what kind of business would send mail to you without you having
agreed to receive it? Not a very honest one, I'd assume (though I
cannot refer speccifically to this one), and not one that is committed
to fight spam and adware.

Now, specifically, regarding Ad Eliminator and the offer that you
might have received, as PinkFreud has mentioned, there is a warning
regarding this software and the honesty of the people who sell it on
TechStuff.ca:
Beware of Ad-Eliminator
<http://www.techstuff.ca/archives/871.html> 

In fact, a review on this software claimed that : 
"This basic adware-removal tool fails to hold its own against numerous
competitors, largely due to its ironfisted trial limitation.[...]
Ad-Eliminator makes quick work of scanning a PC for adware, a nice
plus considering you won't find any extra features such as real-time
monitoring or browser-hijack prevention. The utility hogged too much
of our system's resources while doing its thing and thus caused our PC
to slow down. But the really bad news is this program won't remove any
of the spyware it finds unless you pay to register the full version.
Since you can find quite a few free utilities that remove malicious
applications from your machine, we'd point most users in another
direction. " (SOURCE: Download.com, a review on the software that is
not online anymore, since the site does not offer the software, cached
version on <http://216.239.39.104/search?q=cache:3Vq4jqcSwgIJ:www.download.com/Ad-Eliminator/3000-8022-10305608.html+%22ad+eliminator%22&hl=en>).

A blog specialising in spyware also labels it as suspicious: 
Spyware Warrior <http://netrn.net/spywareblog/archives/2004/08/02/> 

See also the Spyware Warrior's forum
<http://www.spywarewarrior.com/viewtopic.php?t=4443> 

I hope this answers your question. Please contact me if you need any
further clarification on this answer before you rate it.

Thanks for your answer and specifically for the web sites about
Barbara Bullard and ad eliminator. You are right that, unfortunately, 
most unsolicited emails victimize unsuspecting computer users. But I
must differ with you that ALL unsolicited emails are fraudulent or
wrong. I rcently bought some computer ink cartriges in response to
such an unsolicited email, at a much cheaper price, and am fully
satisfied with it.

looks like spam mail.

You may find this useful:

http://www.techstuff.ca/archives/871.html