Yeah, you're not gonna pay for 90' of #6 copper. You have better things to do with that money.
Here's the first question. Do you have any excuse to want power for other things out there? Because now is the time. Right now, the cost of bumping the feed size to support more stuff is practically nothin'. For instance to go 90A instead of 50A, we're talking maybe $20 more in panel and $50 more in wire if that.
Wire types
First, avoid NM and UF cable types for large sizes, as they are not thermally rated, and require a larger size wire to do the same job. (at 30A or below it doesn't matter due to NEC 240.4(D)).
Copper is Right Out. Aluminum works fine for feeder, and is far cheaper. The breaker in the main panel is rated for aluminum, and the supply lugs on the subpanel are most likely made of aluminum (for very good reason: AL lugs can support Cu wire if torque is right; not the other way 'round hence some problems in the 70s). I prefer same-metal on lug and wire, when it's outdoors and subject to wide temperature swings. AL works in feeder.
For only 100' of run, voltage drop will not be significant at 240V, and I see no need to enlarge the wire.
Since you're running conduit the entire way, you might as well use individual wires - easier to handle and smaller conduit. (e.g. #6/3 UF cable requires 2" conduit for Pete's sake, no thanks!) The individual wires will be either THWN or XHHW types (most THHN wire is cross-labeled THWN).
If you want to power just the hot tub, then I would make the long run 6 AWG aluminum (not NM or UF). That is good for 50A, and will be on the order of 20 cents per foot per wire. At #6 or smaller, neutral must be natively white wire, ground must be natively green. (and can be #8AL or #10Cu for 50A).
If you want to power other stuff, my go-to wire is pretty much #2 aluminum (90A). It's dirt cheap, and at at a power/pricing "sweet spot" (#4AL is only 65A and barely cheaper). You'd take that to a generously sized subpanel of at least 12 spaces, and put a 50A/240V GFCI breaker in the subpanel. That will provide your hot tub breaker.
The breaker at the main panel can't exceed the wire/cable rating. So 90A for #2AL, 50A for #6AL or #8Cu.
For the run from the subpanel to the hot tub proper, look closely at the terminal ratings of the hot tub. If they are rated for aluminum and 75C thermal, you can use #6 aluminum cable (not NM or UF). If they are rated 75C thermal but not aluminum, you can use #8 copper cable (not NM or UF). If they are not rated either one, then you need #6 copper and using UF is ok. Ouch though.
On conduit burial
NEC calls out a general "best practice" (18" cover with PVC; 6" cover with RMC except 12" under a vehicle path). However, your local permitter/inspector is well familiar with the soil in your jurisdiction, and will override/adjust those requirements to suit practical reality in your town.
That's what you have to go with. You are not allowed to "freestyle" your own standards.
With rocky soil, conduit is mandatory because direct-wire cable will just get crushed. Even with conduit there aren't good answers, as PVC Schedule 80 can get crushed too, and RMC is expensive ($3/foot) and rusts out if it lays exposed to water long-term.
I wish I could say more, but the simple fact is, this is something you have to haggle with the local AHJ.
Keep in mind that when using conduit as a wiring method, you need to assemble and anchor the entire conduit run, complete, before pulling in the wires. You do not assemble conduit over the wires stick-by-stick. (in order to do that, you'd need to use a legal cable wiring method such as MH or UF, and use individual conduit sticks only where physical protection is needed.)
