I don't know whether I want to stain the bed at all. I like the color of natural pine, and staining it would be additional work.
I'd certainly be in favour of not staining myself. It's not only that it means the pine is used as pine (not trying to pretend it's something else) but it and other similar softwoods are notorious for staining badly, giving awful blotchy results. So staining can make the wood look worse, hardly the intent.
Google research originally brought me to Waterlox Tung Oil finish, and I think the oil finish look is something I'd like, but the long curing time has given me pause.
What are my other options? I'm not averse to using a more generic Home Depot type product if it will look nice and protect the wood, especially if it will work faster without being too difficult.
I was going to recommend an oil finish myself for ease of application and generally being the simplest of true finishing options. Merely waxing the wood is one of the simplest options of all if aren't leaving the wood bare, it provides nearly no protection to a functional piece (why it's not classed as a finish in its own right by many people) although it's fine for small things like decorative turnings and boxes.
The simplest of all oil finishes are actually plain oils of vegetable origin (nut or seed oils) and a key benefit of them and not a wood finish or polish of some kind is that oil is the sole ingredient.
So there are no solvent vapours or other VOCs to worry about, making it ideal for application indoors in a domestic environment. Cleanup also doesn't require solvents, just soap and water is all that's needed. In contrast, Tung Oil Finish will typically have a large solvent component (usually accounting for more than 50% of what's in the tin!) so it has a very pronounced solvent odour.
The principal finishing oil is linseed oil, specifically what's sold as boiled linseed oil (BLO for short). There is also raw linseed oil but this dries very much more slowly and has different uses.
The other main option is tung oil, this gets many recommendations today which I think personally are misplaced*.
So I would very much recommend BLO. I should mention that boiled linseed oil does have a characteristic smell which some people don't like, but many adore it.
Info and tips on applying an oil finish from previous Q&As:
Why is there a progressive reduction in oil for finish/maintenance? Is it necessary?
How do I prepare and take care of a wooden countertop?
Safety note: when working with BLO you must be careful of any application and wiping rags or paper towels. Don't leave them bunched up as they are a fire hazard. Leave them to dry flat on the floor if you can, or draped over the back of a wooden or metal chair, once stiff and hard they are safe to dispose of in the household waste.
This previous requirement is however a problem:
I would certainly hope that glasses don't leave permanent rings on the desk. I'm not 100% sure how I feel about polyurethane's look and feel.
An oil finish is not water-resistant. About the only thing you can apply that is virtually guaranteed to protect the wood from sweaty glasses is varnish unfortunately, with polyurethane being one of the best (and easiest to buy) choices.
So for your purposes consider varnishing only the desktop portion. It isn't uncommon in furniture work to finish tabletops with a full protective finish and have the legs and other components more lightly finished.
Varnishing conventionally to a high standard is not easy, but there's an excellent workaround for that these days and that's thinning the varnish and wiping it on. This converts a regular varnish into what is sold as wiping varnish. It's much easier for the novice or first-timer to achieve a great finish with wiping varnish.
More details in the following Q&As:
What is the difference between wiping polyurethane and wiping varnish?
Protecting against water damage
The characteristic look and feel that I think you're not a fan of shouldn't be a problem if you wipe the varnish on. If you do end up with a slightly glossier finish than you'd like you can reduce the shine very effectively by wiping the surface down lightly with a nylon scrubbing pad/pot scourer (clean of course!) Use light pressure and stroke in the direction of the grain.
*There is no real benefit to using tung oil for an interior piece — it's more difficult and slower to build up a good finish (slower in the sense of taking longer to do as some sanding is part of the recommended method), it dries more slowly on top of this so the wait times are longer, plus on top of it all eventually it ends up looking the same as if you'd used BLO. And you pay more for all of these advantages :-)
Tung oil is reputed to build up to a more waterproof finish, but there are faster and more reliable ways of achieving that end.