It shouldn't affect the fruits that season... If you save the seeds and grow them the next year, you could possibly end up with some hot bell peppers or some mild hot peppers.

you can grow them right on top of each other and it doesn't affect the current year's fruit. Only seeds--possibly.

It is genetically impossible for the bells to be hot growing next to hot peppers.

Also, it is my understanding that most solanums (peppers, eggplants, tomatoes, ground cherries, etc) are largely self-pollinated, often before the blooms open. So, while the bees may cross them somewhat, by and large, I guess they are mostly not going to be crosses. I guess that explains why saving heirloom seeds from tomatoes is relatively easy.

If you want to be sure, you need to separate or cage them, of course.

Tell your co-worker, Alamo, that she is eating the ovary of the plant when she eats a bell pepper . . . !!

The seeds, however, are the plant's offspring.

If there is concern about a crossing with the male flower of a hot pepper, remove the seeds from the bell and discard.

digitSteve

Cross pollination is one of the most misunderstood topics when it comes to gardening. As has already been mentioned here, you wont see the result of cross pollination unless you save the seeds for next years crop. At that point, you'll see the results when they fruit

As pretty much everyone said. It doesn't matter unless you want to save seeds for yourself to grow peppers next year. If you are not saving seeds, plant away, your coworker is wrong.

Peppers do cross pollinate fairly easy in close quarters. Their flowers are much more attractive to pollinators than the closed blossoms of tomatoes.

If you want to save seeds for next year(if you are growing OP varieties and not hybrid, that is a whole nother discussion,) a distance of about 500' is recommended. Shorter distance with lots of other flowers in between to interest pollinators and on opposite sides of a building can help shorten that distance and have fairly good isolation results.
Remy

I was gonna say uterus, digit steve...yumm ;~) But yeah, when you eat a fruit, ie something with seeds in it, you're eating the mother plant's reproductive organs, only the seeds are mixed genetically...

That said, i think this story persists because you CAN get hot seeds in a crossed sweeet pepper, plus a stressed sweeet pepper can develop hottish seeds and membranes even if it isn't crossed.

Exactly put right by digit. I have said the same thing somewhere before.

Cross pollination can only affect the seeds which are the next generation.
So , if your bells' seeds tast hot, then it has been crossed with somes chilie.

As everyone has indicated (but I'll add my 2¢ anyway) you won't get hot bells growing next to serranos nor will you get sweet serranos growing next to bells (at least not this season). Proved it last year. Had my partner look it up on the Internet to make sure. Got our info I think from TAMU website. All my peppers tasted like they were supposed to taste. Serranos were hot and spicy and bells and sweet cherries and pimientos and cubanelles were nice and sweet. Had we saved seeds for next year? Most likely a different story.