There isn’t any reason under 501(c)(3) rules that you would be required to use competitive bidding to purchase goods or services.  There may be a few rare governmentally related (c)(3)s that are required or otherwise have decided to use competitive bidding, or a few organizations required to use bidding under a government or foundation grant. But it is not required for the ordinary 501(c)(3).  Competitive bidding is not necessarily a bad idea, but it is seldom legally required.

If you are a public charity considering a purchase from a “disqualified person,” you may want to utilize competitive bidding to assure that you avoid an excess benefit transaction.  But even there, if there are clear cost comparisons available without bidding, it is not necessary if you can document that the price to be paid is “reasonable.”  (See Ready Reference Page: “Charities Must Avoid Excess Benefit Transactions”)

In your case, you may save a few dollars with a competitive bid on your printing.  But I must say that I am a little suspicious of sales people who, unless they can cite a specific requirement in your case, appear not to know what they are talking about.