She may very well be just fine & dandy by herself.
I got my 2nd (well, 3rd) horse to keep my TB company after DH’s TWH died just before I could move them both home.
TB had been race-bred, failed his 2yo speed test but was kept by the trainer as a pony horse until I bought him as a 6yo.
Boarded for the next 15yrs so I imagine he was never left to himself.
I had not had both home a year when I took #2 camping for a weekend, leaving TB solo.
Neighbors had horses, but all too far away for him to do more than see from a distance.
Campground had no cell service, so I spent an anxious night before I could call farmsitter to see if TB was dealing.
He was fine for the full 3 days I was gone.
And continued to be fine whenever I took the other anywhere,
#2, OTOH, stressed when I took TB away - pacing the fenceline & calling.
But he too lived to tell about it.
There’d be some “parts” sniffing when I brought the traveler back, some squealing then back to Business as Usual.
Your mare will let you know if she’s okay alone.
Give her at least a month to settle & then reassess if you need a companion or not.
If you have room for 2 a pasture-board retiree might be a cheap option - just feed & routine vet/farrier care (paid by owner).