If I am the executor and trustee of a will that states the house must be sold, can I buy the house if I outbid the realtors would be buyers?

Well, there are issues with that.  Generally, there must be approval by all the beneficiaries, especially if it would benefit the estate (i.e., more money in the estate).
Here is some information for you to review:

Sec. 348. PERMISSIBLE TERMS OF SALE OF REAL ESTATE.  (a) For Cash or Credit. The real estate may be sold for cash, or for part cash and part credit, or the equity in land securing an indebtedness may be sold subject to such indebtedness, or with an assumption of such indebtedness, at public or private sale, as appears to the court to be for the best interest of the estate. (emphasis added).

You may with to bring in an independent executor to ensure the other beneficiaries' interests are covered.