You may have both over-watered and under-watered. Twenty minutes at any one time sounds excessive, and once a week in the San Diego summer may be too little. Bamboo like to be continuously moist, but not drowned; you do not want the soil to be dried out. I think you need to do shorter and more frequent waterings. You should also consider mulching around the base to help conserve moisture. In addition, buy yourself a cheap (under $10) moisture meter at Home Depot and use it to keep an eye on moisture conditions in your soil. Bamboo are generally pretty tolerant of moisture variations, as long as you avoid extremes.

I have a few diff bamboos. Old Hami which is big timber and a couple of bushy varieties. Both are in the ground and seem like can't get enough water. I am in riverside tho where it is over 100 degrees. I have a watering system with 3 outlets which waters about 3 gallons and hour. It comes on for 10 minutes 3 times a day. Since the start of summer, my old hami has 4 new 20 foot tall shoots & the leaves are big and green. Some do die, but new growth is frequent. if the leaves are curled, it needs water. if you see new growth, you are fine. If you have it planted in the ground & in well drained soil, I dont see how you could over water it. It's a grass!

Sounds to me like the symptoms of fertilizer burn. Otherwise, possibly, if the plant has been in the same pot for a while, it has filled up the pot with roots and you have lost the water holding capacity of your soil. In that case watering once a day is too little, even if you water it for 20 min it can only take up so much water over a 20 minute time period and then becuase the soil can't store the extra water it dries out long before the next 20 min watering. Try watering more often for shorter periods. Or else put it in a bigger pot with more soil. You really can't overwater bamboo.