Volaris airlines flies Tijuana - Hermosillo nonstop, see
here. Probably your best bet.
VivaAerobús flies from SNA / Orange County, but you'd have to fly to MEX and back up to Hermosillo. Interjet can't get you there from SoCal.
Next, I'd recommend a First Class or Comfort bus from Tijuana for this. 13:00 hours, roughly.
I've driven that, and it's a long day's drive. Perhaps an overnight deluxe bus would get you there without losing a day, safely and in relative comfort.
See the timetables for various bus lines
here; for night bus, the Comfort or zconfortvservice, MXN 785, would probably be your best bet.
TAP (Transportes y Autobuses del Pacífico) offers busses with 36 seats, air con, wifi, onboard coffee machine, six video screens, toilet and air con, for example.
TAPRoyal is an international bus service from Los Angeles with 57 deluxe seats, etc. check their website in English
here. In downtown LA, they depart from 767 MAPLE AVE. LOS ANGELES CA. 90014 (213) 533 8700.
Elite offers 36 seats, two toilets, five dideo screens, leg rests for your seat.
TUFESA also does L.A. downtown to Hermosillo. Leaves L.A. Nine pm, arrives noon the next day. I'm unfamiliar with this line.
I've been riding Mexican buses since the 1960s; first class and above and they're safe, reliable and beat the slats out of most bus services in the US.