The days when the corner drugstore carried OK, plastic-backed disposables are past. Many stores are shifting to only carrying the lower-end disposable underwear, briefs with a "cloth-like" backsheet, or some other undiaperlike euphemism. Of course, the higher end diapers have greatly improved and continue to use a plastic backing for odor containment, but typically are only available by delivery. This is a problem for AB/DLs who don't wish to risk having large packages with pictures of diapers on them arriving at their doorstep.
However, there are still a few places in the Bay Area where plastic-backed disposables are available over the counter.
Since some cities have banned free shopping bags, and some chains have stopped offering them even if they aren't in those cities, it is a good idea to bring your own bag if you are buying a bag of diapers. On the plus side, this gives the shy an excuse to carry the diapers out in their own fully opaque bag. Cases usually come in brown cardboard boxes with limited markings.
A-Abco has closed down their medical supplies branch, choosing to focus on their non-medical rental business, also in Redwood City.
425 S. Bascom Avenue, San Jose, CA 95128 (They moved across the street and up a bit): This shop carries Molicare (plastic-backed, but purple) and Tranquility ATN. (Sadly, Baby Land Furniture has closed down.)
This Redwood City company receives honorable mention for having products designed for AB/DLs. Their website makes no mention of an option for retail pickup.
165 Lewis Rd, Suite 10, San Jose, CA 95111 Thanks to an an out-of-towner (Gelaï from France) for this tip. DiaperFetch carries Secure X-plus as well as Tranquility Slimline (thin, Medium and larger might still be plastic backed) and Depends Maximum Protection. In-store pick-up can be requested, but they seem to be mainly by-the-case delivery. They do ask for information - name, address, etc. - and enter the information into their records.
DiaperFetch gets bonus points for the fluffy mascot. They also get extra credit for their motto, "Fetching diapers to your doorstep!" Superficially, it is clear that "fetching" was an attempt to tie their mascot in with their delivery service. However, "fetching" usually involves bringing back. They don't carry cloth diapers, so the return would have to be back into diapers in general. Finally, fetching is also an adjective: We're not just to go back into diapers - but charming, captivating diapers - "...fetching diapers..."! That is a lot that can be read into a superficially innocent motto.
Now out of business, this once statewide chain used to carry multiple lines of Attends products.
112 E. Fremont Ave., Sunnyvale CA 94087. This medium-sized supply store carries some good diapers, including Abena M4s by the bag or case. They carry both plastic-backed and breathable Abena products, and their prices are competitive. In a shopping center at the intersection of Fremont and Sunnyvale Saratoga, it is nestled in between a large gym and a large barbecue place. The store itself is hidden behind a gas station, which offers a little extra privacy when carrying purchases out.
They are open weekdays as well as 10AM-4PM Saturday.
37323 Fremont Blvd. Fremont, CA 94536. This pharmacy chain has eight branches in addition to their main location, which is open Saturday and Sunday. It carries First Quality as well as some Attends. The awkwardly named Attends "Waistband" line seems to only be stocked in large, in contrast to the "breathable" line. First Quality is a good to OK plastic-backed diaper, but is color-coded based on size: only the mediums are white.
While not as babyish as Bambinos or First Quality, Depends "Maximum Protection" still has a white plastic backing. It is available from Rite Aid and other places.
Many thrift stores have disposable diapers on their shelves from time to time. Some of these will be old, which might be a plus depending on one's tastes.
Of course, these resources are liable to change over time. Please if you have more recent information.