Absolutely you can. Since you posted a cash bond and did not go through a bondsperson, you will need the court's permission and also will need to file a waiver of extradition with the court. This is a rather common request.
Jay is accurate. There is no prohibition in moving to another state as long as you sign a waiver of extradition agreeing to return to CO for sentencing.
As Mr. Tiftickjian and others have stated, you can leave CO and move to NM, you just need to obtain permission from the Court prior to leaving. As far as entering a plea, you don't hire attorneys to plead you guilty. You can do that for free. You need to consider hiring a DUI Defense attorney to help you address this case and to ensure that you obtain the best outcome possible.
An attorney may be able to appear on your behalf for non-dispositional hearings if you are living in NM. At the end of the day, what is important is the result and knowing that you did everything possible to minimize the damage and consequences. Take advantage of free consultations and talk to several DUI attorneys so that you can make an educated and informed decision on how to proceed.
My decision to answer your question does not construe an attorney client relationship. My opinion is based on the facts you have provided. Before making any decisions, you should always consult directly with an experience attorney, either in person or via phone.