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The ad itself has nothing to do with the minimum bid for a keyword. Each keyword has a default min bid assigned by Google. If you create a brand new account and a brand new ad group with a keyword, you will get the default min bid. Having the keyword in the ad will do nothing to help you here.
The only thing that will lower your default min bid is using established ad text. What I mean is this: If you have established ads in your account, you can use these to get lower minimum bids on new keywords. The CTR history of these creatives are what determine your min bid.
For example, say you have 3 old ads, one with a 5% CTR history, one with 10%, and one with 20%. Now let's say you add a brand new keyword to your campaign. If you use the 20% CTR ad, you will get the lowest minimum bid. The 5% ad will be higher, and a brand new ad that you have never used in your account will be the highest of all. Note that you don't have to put this keyword in an old group, you can create a brand new ad group. You just have to use the same exact ad text.
The theory here is this: Google is rewarding advertisers who have proven themselves. If you have great ads with a long history, Google says okay, this guy knows what he is doing, we will give him a discount on any new keywords he adds as long as he uses one of those great ads.
Here are a couple of twists: You can actually alter your ad and still get the discount, but it will be lower depending on what you change.
Change Title: Highest
Change Desc 1: Med
Change Desc 2: Med
Change 1 and 2: High
Change Display URL: No Penalty
So that is what causes people to get different minimum bids on the same keyword. I am guessing your overall account history is tied to your default min bid as well, with additional discounts being applied for using specific ads in your account.
I haven't yet figured out a way to take advantage of this. Maybe it's best to create new campaigns on established accounts rather than creating a new account. I haven't tried that yet.
This whole system is designed to eliminate spam from the results. Step 1 was removing affiliates, step 2 was removing the bottom feeders. I kind of liked how it was right after they removed the affiliates. But the system is just too big these days to allow everyong 1000 impressions before the system does something.
Anyway, to summarize, if you want the lowest possible minimum bid for new keywords, use your best all-time performing ad text. Obviously if the ad doesn't make sense for the keyword then you have a problem. But remember, you can tweak the ad and still get a discount.
Keyword 'widgets' has had a minimum bid of $5 since the change to the new algo.
I created a new adgroup with 'widgets' as the only keyword, and created highly targeted ad text with the keyword in the title, description and both urls. Min bid $5
I then created another ad group, again with 'widgets' as the only keyword. This time, the ad text was copied and pasted from my best performing ad with a CTR of 34%. The ad text was completly irrelevant to the keyword, and what do you know? min bid $1
obviously that's not enough to draw solid conclusions from, but it's enough to make you think...
I am building a database of 9000 of my most important keywords and all the ads of all my competitors, and monitoring which ones are there consistently for that particular keyword.
I constantly split test ads and I have found that when you get to the point of maybe 6 months running the same ad, you seem to have a "grandfathered" quality score, in other words you can bid a lot less, your ads are shown a lot more, and life is good.
I will see if this ad text thing actually works "cross industries" like if one ad that works great in one industry actually works in another industry, which would definately help making high CTR ads easier to make.
If true, this 6-month factor could be an attempt to severely discourage slash-and-burn/drive-by/dictionary-dumping "new and used dead popes for sale" ads by new users (or on new keywords) without penalising long-standing users with well-performing ads.
If so, I'm in favour.
The lesson to be drawn from this is to change/add things in your account slowly (and spend time observing behaviour) rather than chucking in the whole Webster's/OED on the off-chance.