Here are some suggestions for a research plan to get you started.
First, a basic principle: Most records that we use for genealogy (such as church records or government records) were not created for genealogy, but for a different purpose. They are usually mandated by a law, and we can learn more by finding the law which says a record should be created and collected.
Suppose we wanted to start with the current-day state law and step backwards. We might do this:
Step 1: Understand the process of opening and closing a business, if the events took place today.
Information intended for current-day business owners, like this tutorial for starting a business in Colorado or this checklist for new businesses from the website of the Colorado Secretary of State, can show you how the process works now, and give you examples of names of documents that you might want to search for.
Step 2: Locate the relevant state statutes for today and work backwards through the changes in the law until you arrive at a point slightly before 1905 when your business opened. University of Colorado Boulder's Law Library has an online guide.
Step 3: Read the statues, and make a checklist of what records were required.
Or you could go to the state statutes for the period before 1905 and search there directly.
Check all jurisdictions
Do records exist at the Federal level, the state level, the county level, or the city/town level?
What might be in the archives?
It helps to understand the life cycle of any record. Records are created for a particular purpose, and there are usually rules about how long it has to be retained by the agencies that created them or collected them. Those agencies have custody of the records until they either dispose of them, or give them to another agency like an archive, library, or historical society. Very often the time frames for when a record is disposed of or becomes archival is expressed as a rolling window, so many years past some specific date since the record was created. If the conditions for the rolling window have not been met, the records won't be in archives yet -- they'll still be at the agency where they were collected or created, assuming they weren't discarded.
It's also possible that records had been created but weren't deemed of interest. For an example: Bankruptcy case files held at the US National Archives have recently been consolidated in Kansas City: see Bankruptcy Case Files at the National Archives at Kansas City. You can learn more about the nature of the records by viewing Jessica Hopkins' presentation "Broke, But Not Out of Luck: Exploring Bankruptcy Records for Genealogy Research" from NARA's 2015 Virtual Genealogy Fair (bearing in mind that the records have moved since she gave her talk, so her advice on where to find them is outdated). But in a recent APG webinar on NARA Kansas City, a presenter said that not all the bankruptcy case files are retained by NARA, so researchers looking for records of bankruptcies should consult NARA Kansas City for more information.
For private papers that may have ended up in a manuscript colletion in a participating archive or library, check WorldCat's sister site Archive Grid.
To find legal notices in newspapers, find out what newspaper in the area was the newspaper of Record. Use directories like Chronicling America's U.S. Newspaper Directory, 1690-Present to find out who holds the newspapers and like The Ancestor Hunt's Colorado Online Historical Newspapers Summary to see what papers are online.
Before you start to look for the records themselves, look for research guides and finding aids. Lisa Louise Cooke's site Genealogy Gems has tips here: Google for Genealogy: Google Keyword Search Tips. Try using keywords such as historical business research guide finding aids in addition to the locality names.
In addition to the Taxation records mentioned in the earlier answer, in the FamilySearch Research Wiki, look for sections titled Business, Commerce, and Occupations in the county-level pages. Many pages don't have any information in that section yet, but you never know what's there unless you look.