Having seen them I know that there are some small-bike rentals down in southern BCS . They are hard to find on the internet because every google search seems to wind up with some state-side Harley or BMW rentals and expensive long guided trips from Arizona and California and Nevada $$$ .
I did locate some in Baja by going to GoogleMap and then asking about dirtbike rental locations .

With the flexibility in scheduling of time and location you describe it might be just as easy to fly south to the Cabos and La Paz to see what you can find in the way of small dirt bike rentals. If it pans out ,great , if not your girlfriend can always learn to ride in Quebec .
The rental businesses usually set out a selection of small bikes and quads under a sunshade on or near a beach or near a resort hotel , with a bunch of flags and banners to draw attention . They rent out at an hourly rate so you could sign up for a full day , come back for more if you liked it or try at a different location .
Their target customer base is the youth who fly in with little to no experience in operating a dirt bike or quad but who want to goof off on the beach or use it for personal transport around the resort . This is the type who show up on "Funniest Videos " as they grab a fist full of throttle and wheely a moped straight into a hedge on their first try. "Its a tiny bike , eh ? . What could be so difficult ? "

Just outside Todos Santos I was riding my own bike on Mex 19 when I noticed such a rental company so I stopped to observe . They were setting out to give a group of tourists on small quads a guided ride around their desert property trail . It was clear that most of those riders were absolute first time riders as they repeatedly stalled their engines , rode into the brush or got stuck in a sandy dip after going over the bars. The tour guide /instructor was quickly exhausting himself by babysitting them , running his bike up an down the line repeatedly yanking quads out of their predicament while the group did not make much headway . ( I am trying to get a picture into this email, did it once before , but I forgot the convoluted steps required here )

Most of the renters offer quads , or only quads because the novices are less likely to break their own body sitting strapped into a four wheeler . There are such services shown at San Jose del Cabo, Cabo San Lucas , Todos Santos and along Mex 19 midway between CSL and TS .

At Todos Santos this next company , Nomadas Drift ,has a website and advertises actual dirt bikes and a social, experience ( not my cuppa ... and probably very $) .
Have a look

https://www.nomadasdrift.com/

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Thanks @Sjoerd ! I think that will indeed be our best option, ie fly down, and check out the day rentals on-site.
Was it a photo of a whiskey throttling tourist on a quad you wanted to upload?

By golly ,I surprised myself . With some probing and patience I managed to "download " two paperclip-connected files . In the composing step they only showed the number of the file , so I was dubious as to any success . So I posted and they really showed up here as actual pictures .
First image is the rental company location with the quads setting off into the trail.
Second image is of the bikes into the trails a short distance and already the tour guide /wrangler is having to aid the clueless riders . The horse riders appeared to be using the same trails but they probably really don't need to rein the horses because the animals are self steering around their familiar terrain . They will auto-pilot it back to the feed and water supply .

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