It depends where you are crossing. I can tell you about Arizona only.
Agua Prieta has a secure parking lot with a gate and at times, helpful "helpers who will promise to watch your stuff for a tip. Never had a problem - 10 peso tip will do it. I think the Aduana folks have chased these guys away
At Naco - Banjercito (permits) is only open Thursday afternoon through Sunday night - you will park right outside the door. You can get a visa in Naco 7 days a week.
Nogales at km21 Never a problem there, lots of agents wandering around.
In any event, if your boxes are locked and your stuff tied down no one will bother you. I have used a cable lock for my helmet and jacket in the past. Run the cable through the sleeve and the chin bar an cover up the luggage with it. Naco is usually pretty quick because no one is there. When the Banjercito in Naco is closed, you can get a visa at migration there then go 20 miles to Cananea for the permit. The too are rarely busy and the elementary school guard will watch you bike.
You will not have a problem. Many solo riders cross all the time.