Bob: When I head to Yosemite from San diego I go through Fresno and stop at Oakhurst for the night (Hwy 41 all the way from Fresno to the Park entrance). If I recall correctly, it’s about 45 minutes from Fresno to Oakhurst. Then the next morning, I head out early (6:00 am) from Oakhurst and reach the Park entrance in about 15 minutes. From there, it’s about another 45 minutes to the Valley (avoiding traffic this early). Go straight to the Wilderness Center in the Village to get your Wilderness Permit and directions/parking pass to the backpackers parking lot clostest to Happy Isles (about a mile from the trailhead). I would go early (if you can) as it’s a zoo on the trail at Happy Isles for the first couple of miles or more, particularly if you decide to take the Mist Trail. The John Muir Trail will be the less crowded alternative to the top of Nevada Falls.
Having said that, in direct answer to your question, if you’re going straight from Fresno to the Valley at 10:00 am, I would assume at least 2 hours, depending upon the traffic. By the time you check in at the Wilderness Office and get to the trailhead, assume another hour, at least. Hopefully, you can be on the trail by 1:00 pm or 2:00 pm latest.
Have a great hike!!
Sherpa Steve