In America, we may say bad reputation, but for their culture, it is not tardiness but standard (same with the Hispanic community, to some degree). That said, it is a fair worry, but I'd say, if you haven't anywhere else to be, use it as paid practice time!

If you expect this to happen, I'd agree: go hourly. If, for example, a normal wedding takes two hours from prelude to postlude, cut your normal rate in half and call it your hourly rate. Then there's nothing to loose.

I think the hourly rate thing is much less likely to offend than the I-have-a-later-appointment thing.

Might I offer the caveat of caveats?
Work with the celebrant as far in advance as you can (both weddings and funerals.)
It is their preview and provenance that should be engaged prior to the event that determines, ultimately, the length of the service.

I agree with working on an hourly basis. [ I don't that any particular race can claim the monopoly on wedding lateness. My experience was with a white bride who arrived 45 minutes late.]

I concur with Mssr. Bourbon and JQ. For the first half of my 45 years as a music provider I was still too green to be paid before the wedding, and was stiffed enough times to "get it." I don't want to be paid until the wedding day, so the wedding coordinators diligently collected the stipend at the rehearsal, notified me of transaction, and we were good to go.
If you bill hourly, what happens afterwards when you're at the console two hours in, an afterwards you have to rush about finding whomever has the chequebook? I realize protocols can be put into place at the office to minimize such concerns, but that increases the number of personnel who'd have to track the money trail, or follow up with the bride's dad (presumably) to recover any discrepancies.
Once again, I advocate the return of the public wedding sacrament being folded into a scheduled Vigil/Sunday Mass. Lotsa positive outcomes in that solution, not the least of which is the loss of "This Mass is all about meeeeeeee!!!!!"

Well, the Catholic Church, we're more in Rome than the USA. How would a Roman handle this situation?

The last late wedding I experienced was because the bride was having difficulty ladling herself into her dress.

And you know this how exactly? ;-)

We arrived 20 min. late because we got lost, but the wedding was 30 min. late. We were told that's why (dunno if it was grooms' or brides' people). And it was pretty obvious that it didn't really fit. It was at the U-Us, but I heard the "forever" word, so it was all good with me. (Seems that if we're going to get opinionated about the sex aspect of 1M+1F4Life, then the duration and number aspects are equally fair game.)

As a student, I played for weddings one year--fifty weddings that year. I quickly adopted a maxim: up to 30 minutes, the wedding is not even late yet, and these were hardly Africans. It was very often the bride, who was late. Not having done this before, she had no idea how long it would take her to get ready.