I would like some advice as to what to say if I bump into SO's friend in a hotel.  I have no business being in a hotel, and can not think of anything but please don't tell my SO.  So far so good but always nervous it may happen.  Thanks for any advise.

you can say you are picking up a client for a meeting.  Not being in the business world, I can't think of anything else.

Swim

This is one reason why I like big hotels. They always have business meetings going on. Conventions. Conferences. Luncheons. Awards ceremonies. Find out what's happening at the hotel and THAT is your excuse for why you are there: "I am attending the Retail Purchasing Managers Association Conference in the Laguna Ballroom. Fascinating stuff!"  

Is she a provider?

Do not park on the street.  If people you know work at a certain facility or have business there...  you go somewhere else.  This is basic.  
A certain provider is working at the hotel in town...  right next to the interstate entrance...  Duhh!!  Friends, family, neighbors all driving by.  Sooner or later, one would spot my car or see me driving in.  I drive 45-60 minutes to the city & see other providers.  (Even dogs are smart enough to not crap where they sleep.)

I know it hard to do, but never hobby in your own back yard. Don't hobby in the city or county that you live in. You reduce the probability that you will run into someone that you know.

there to see a sales presentation (like insurance), attend a business meeting of some kind, or to meet a colleague for lunch, drinks, etc.  If it is a mid-level hotel your options are limited to the last of the previousl list.  Might we wiser to play in a neighboring town.

Sy that you are meeting an old friend from high school or college. Regardless of what you do, say that you are there to discuss some aspect of the business you're in. If you run a jackhammer during street repairs, say that your boss asked you to come to review new jackhammer models and there you are there to talk to the saleman that has the models. Just have a tall tale about what you looked at during your meeting with the saleman.

Never use someone else as an alibi...   some details are bound to be different & puts the friend on the spot & complicit in your lies.  
Back in the dark ages before cell phones, my ex & I had been having some troubles...  she began acting out.  Ex had this GF who was separated & going through a rough patch.  One night I discovered she was not home, decided to drive out to see the GF late.  GF talked to me & it being too late for me to drive home, she had me sleep on her couch.  (GF & toddler grandson had the bedroom).  In the morning, the phone rang.  GF motioned me to listen in & held the phone off her ear.  It was my soon-to-be-ex...  she'd already tried calling MY house but, of course, I was not answering.  Wanted GF to call until I answered & lie that she'd spent the night with her.  GF says "I can't do that!"  S-T-B-ex, says "Why not?"  GF:  "Because he's standing next to me!"  
Shortly after this the GFs husband took me for a ride, pointed out the bar & the motel with my car parked out front where she was shacked up...  I figured that was irrconcileable differences if ever I saw them.

Don't park your custom Ferrari out front to be spotted!  In the door & follow the directions you asked the provider for, straight to the elevator.  You need brass balls but you are only in the lobby a few seconds.   Now if you are at convention hotel, you might have an excuse to meet a client who is staying there...  in the bar or resturant.    
skb

and it is not all about SOs.  Too many people in my city I have no desire to meet when I am on a date.  That's what they created airplanes and highways for.