|The following is based on information from Van Buren design documents and is not canon.|
Governor Dodge will not see every Tom, Dick, or Hairy Mutant who staggers in from the wastes and asks to see him. That's why Dodge's right hand man and commander of the Hoover Dam NCR, Major Jack Fleming, will be the player's initial contact with a high ranking government official at Hoover Dam.
Character type completion breakdown
Combat, Diplomacy, Stealth Boy - Jack believes actions are louder than words and will only let the player to see Dodge after the player has proven himself safe, sane, and willing to help Hoover Dam. The first two can be camouflaged, but the last will require actual player action. The player may choose to work for the Crimson Caravan Company and earn a good working reputation from the company's head, Ailis McLafferty. Doing a couple of caravan missions and earning her trust will give the player her recommendation to see Governor Dodge.
Another way is for the player to work for 3-Some Caravan Company, accept their offer to find evidence of misconduct with Crimson, and then expose Crimson for the two-sided shits they are. This will not only please Dodge and company to no ends, but it is a huge step towards peace with the BOS.
Science Boy - Finally, doing some old fashion science can help here as well. If the player is a science of mechanical wiz, they can apply their skills in helping the former scribes create a better filtration system to make the irrigation water drinkable. The player will need schematics from Jericho, but if the player does the upgrades himself instead of just handing over the schematics to the scribes, then the player will be a hero and earn the right to see Dodge.