If you don't mind a little blush white and want an Old Garden Rose, than I'd suggest 'Coquette des Blanches', linked below. For a more modern rose and more white, maybe 'Paloma Blanca'? 'Marie Bugnet' is a nice, well-behaved Rugosa, but I don't know how she'd do in your climate.

Here is a link that might be useful: Garden Musings blog on Coquette des Blanches

I have had good luck with Sugar moon. You can find it in Chamblees website. It is pure white and very fragrant and it has been very healthy.

Ducher is almost constantly in bloom in Houston, TX - both at my home at at the homes of friends. Blooms are smaller in the heat of the summer. I think it is a wonderful rose.

A white polyantha rose I like is Katherina Zeimet. In your climate you could also look at beautiful teas and noisette climbers: Puerto Rico and Aimée Vibert, for example. There is so much to choose from.

I am attaching a link to previous thread on the topic from last year.

Good luck.

Here is a link that might be useful: white thread

Thank you for the suggestions. The form on aimee vibert & coquette des blanches look nice. Since ducher is earthkind that's a plus as well. Thank you all

'Bolero', 'Snowbird'.

Ducher is a great rose; I highly recommend it. I just planted Bolero this winter and is great so far; love it!

Did anyone mention Iceberg? It's everywhere in So. Calif but for good reason; it's one of the great roses of all time.

Iceberg is my favorite. Even the malls have her planted here. There are several planted along one Jack in the Box drive thru !

Small: Marie Pavie
Medium-large: Devoniensis.
Very large/climber: Madame Alfred Carriere

Just to complicate matters and enable you, I thought I'd chime in, too. All the ones mentioned in earlier replies are great, too. Carol

My usual recommendation: 'Madame Jules Bouché', an old, Tea-rose-leaning HT. An extremely easy, vigorous grower, fragrant, lovely blooms. She does get a bit of mildew but isn't bothered by it. Truly a fabulous rose, grown, I am told, as a passalong plant the length and breadth of Italy. I got my first cuttings from a neighbor and see it here and there locally. It grows easily and vigorously from cuttings, is a frugal, tough, floriferous rose, but if it gets tolerable good culture will yield opulent blooms. It should be pruned lightly, like a Tea.
These other recommendations are good too.
Melissa

'Kaiserin Auguste Viktoria' is another, if you can find it. Nice fragrance, pretty flower. Also a climbing version available.

WHERE in SoCal you are located -- matters.

Jeri

Iceberg is, everywhere. It really is. I see it bloom all the time. The fragrance part, that's a downer.

Thank you everyone. These are some really great suggestions. Now the trial and error.

Jeri I'm located in the inland empire. It gets 100+ here in the summer, which is another problem if I don't want fried roses.

I THINK the ones I listed will thrive in your climate. I've never lived in your area, but the three roses I mentioned grow well in the furnace of North TX summers. Carol

My absolute favorite is Lamarque. Very clean, excellent rebloom, lovely lemony fragrance. It is a climber though not sure if that's what you want. I have it growing on a picket fence. Dutcher would be my second for a white rose as a shrub. .