Your credit report is most definitely not run every time you put an offer on a property. For example, if you apply for a loan with one bank of broker, then go out and make 10 offers, you would typically only have one credit report run. Also please know that now if you shop around and have multiple lenders pull your credit within a small window of time, your score won't drop from the multiple reports being run.
With respect to how running multiple credit reports would affect your FICO score, here is a good free booklet put out by Fair Isaac (creaters of FICO). Page 15 talks about inquiries: http://www.myfico.com/Downloads/Files/myFICO_UYFS_Booklet.pdf
I hope that helps.