If you have a Quality Score of 2/10 then you have the lowest quality score you could earn without having your campaign completely disabled. The reason your first place bid estimate is so high is that your poor quality score, not due to stiff competition. I usually see that low of QS on poorly chosen keywords. If your keywords are too ambiguous then you will not be able to get a good QS.
The fact that you see few or no advertisers on the keywords you are targeting indicates that it may be a poorly chosen keyword, else there would likely be plenty of competition.
Having said that, if you run your ads for a round of 1000 impressions you will get an updated QS based primarily on your relative CTR. If you write really compelling ads that get high CTRs as compared to your competitors, then your QS will improve and your CPC will drop.
Another thing is that you should start with exact and phrase match keywords only. Avoid broad match keywords as they will tend to have more issues with Quality Scores. Also, be sure to use negative match keywords where applicable.
Here are some tips for writing effective ads:
Tips for creating successful text ads – AdWords Help