I had some issues with siphoning last night, so it took about an hour to rack from the carboy to bottling bucket. Should I be worried about oxidation? Both containers were open that entire time.
It really shouldn't be an issue for oxidation. I wouldn't worry about it.
When racked properly only the surface area is exposed. At worse maybe the last couple bottles may have an issue.
The beer is really at more risk of an airborne infection than oxidation in this limited time even at an hour as you said.
Oxidation manifests as a cardboard or wet paper aroma and flavor.
Oxidation only happens when there is alcohol exposed to oxygen. So it's only a concern at later stages of fermentation, racking to secondary, bottling.
Make sure you have a good siphon. Eliminate bubble traps in the line, and get them pushed out asap.
Don't splash. Make sure the line is well submerged.
Use oxygen absorbing bottle caps.
Oxygen exposure can be completely eliminated by proper kegging methods, using purged vessels replacing air with co2.
It may surprise some readers to learn that I pour my beer from primary to secondary fermentation vessel and then (some days later) pour it back to mix in the priming sugar. I then use a "open" siphon with a manual tap at the end to transfer the beer into the bottles. So lots of chance for contamination and "oxygenation". I have done this for several years and with over a thousand litres in many beer styles. I bottle condition the beer for up to 18 months. So I am usually able to check on the progress of the brews for some time. I have not yet found any "wet cardboard" or "buttery flavour" or "damp nuts" or any other "off flavour" in the resulting beers. Yes, "touch wood" indeed! See this link about "Pour beer" for photos of this outlandish technique: Pour Beer!
This has caused concern for some brewers who swear that my beer must be bad or taste off or that I only do this to provoke a reaction. But actually I pour the beer in open air because it is quick and simple. It also seems to help the beer clear and by degassing it before bottling it is easier to bottle (less foaming over).
I don't make this post to tell everyone to follow my example (although please feel free...). I merely make this point to say that "oxygenation" is not (always) the monster it is made out to be and that beer in its natural and unfiltered state is a relatively stable compound. Yes, it can spoil but not usually without some effort and small "mistakes" in handling or exposure to air do not render the brew instantly useless.
As other have said - see how it tastes. If you like it - success!
You might have issues. Taste your beer every week to see how the flavor is developing and keep notes.
I recently had to dump a bunch of bottles that had become oxidized when I racked to the bottling bucket. I too had siphoning troubles and many air bubbles began traveling through the tube.
As the beer aged over the next 4 weeks the smell was always good, but the taste was more and more nutty and "damp". 6 weeks in and the taste wasn't improving, nor was it very good (to me).
If the flavor is good, then I wouldn't be concerned about it, but it might not last as long in storage.