"Miss, sit near the door."
Translation:Señorita, siéntese cerca de la puerta.
Sentarse, the infinitive, means to sit (down). You could use it after a main verb, like "Señorita, (usted) tiene que sentarse cerca de la puerta."
Here we are giving her a direct command, so the usted command changes the -a in sienta to an -e (siente) and the se is attached (siéntese).
I make this mistake all the time. I try to look for the formal indicative form of the verb(the one we use the most so far). For this, sentar, the indicative would be usted siénta, therefore the formal imperative would be siénte and since she is seating herself, siéntese. This has not failed me YET. However I am only 63 days and 234 crowns in.
The reason you would use siéntese is because she is seating herself. It is the same as duchese, levantese, lavese. They are verbs one is doing to themselves. Since no one else is going to seat, shower, get up, or wash someone else, the se would be required. The sentence telling señorita to seat herself near the door. The informal sentence would be Hermano, sientate cerca de la puerta. "Brother, seat yourself near the door." In English, we "generally" tell someone to sit somewhere, not "seat themselves" normally.