What sort of wire should I use to run an overhead line to a subpanel?
You'll need more than 12' of pole and mast for a 12' clearance

The NEC requirement for wires over residential property at less than 300V to ground is a 12' clearance to the ground from the wire's lowest point.  This means you'll need taller poles than 12' to get the wire up high enough.  How much taller? Well, you'll have to consult a sag and tension chart for the cable you're running to determine how much extra pole height you need to meet that 12' mark, or run the calculations yourself (see PDF pages 33-35 of this Southwire install manual for details).

(As a FYI: I was able to get workable tensions in a Hackney/XLP (4AWG Al, quadruplex, XLPE insulation) for a 125' span with 42" of worst case sag, which would mean that you could make the run point-to-point (no intermediate poles) with 16' masts if the path was not obstructed, and still have a few inches of clearance margin left over.)

You may need more clearance yet still

Depending on how your property is categorized by the AHJ, it may be considered logging or farmland rather than residential property, which boosts the NEC clearance requirement for overhead lines to 18' from 12'.  (Basically, it depends on whether the AHJ expects trucks to be driving around on it or not.)

As to the cable itself...

What you are describing (your very own overhead cable run) is termed messenger supported wiring in the NEC, and can be done using a separate messenger and field lashed/bridled cable (such as for a communications cable), or with a multiplex cable designed for overhead distribution service -- really, the same cables that are used for overhead utility service drops.

You will want a quadruplex cable in order to provide a full four-wire feeder -- these cables consist of two hots, an insulated neutral, and a bare ground/integral messenger.  Note that these cables also are generally only available with AA-1350/EC aluminum conductors, so you'll need Al9Cu insulated, outdoor/wet rated connectors (Burndy AGSKIT2 or equivalent) and an inch-pound torque wrench to terminate them properly.

Furthermore, there is no such thing as 8AWG quadruplex cable -- the smallest size it comes in is 6AWG, and since you're feeding a dwelling unit, I'd recommend a 4AWG aluminum/XLP quadruplex instead, which can handle a  100A feeder to the bunkhouse.  This is going to be less costly and time-consuming to handle than trying to wrangle a SE-cable alligator onto a separate messenger, and get you more ampacity for your money as well.

Terminations matter

Overhead cable runs like this one terminate at each end in a conduit mast and weatherhead, just like a service would.  I'd recommend 2" RMC masts -- these provide plenty of space for 2AWG aluminum or 3AWG copper XHHW-2 conductors in the masts for the hots and neutral, and also provide the grounding conductor as well as upgrade space to allow 200A to be provisioned without replacing the masts and poles, just the cabling.

The grounding conductor connections between the messenger wire and the masts at each will need to be made using a jumper (6AWG bare copper is fine), an Al9Cu split bolt, and an Al/Cu grounding clamp (Ilsco AGC-2 or equivalent) -- this setup may seem awkward, but it saves the need to pull a redundant ground wire through a metal mast.

You will also need to ensure that the masts are guyed properly, and that drip loops are provided at the cable ends so that water does not run down the cable and into the mast.

Other notes

You'll need to provide a structure disconnecting means (this can be a main breaker in the subpanel) and a grounding electrode system (given your rocky conditions, you may need to employ a concrete-encased, or "Ufer", grounding electrode -- check with your AHJ for details) at the bunkhouse.  You'll also need to ensure that the bonding screw or strap is removed from the panel in the bunkhouse, as neutral and ground are only allowed to meet at the main service entrance.



If you want to go underground...

This is where things get ugly.  Normally, I'd recommend Schedule 80 PVC, possibly with metal sweeps and stub-ups (you could even go to PVC coated GRC for these for such short lengths; if you don't, you definitely want to tape a metal stub-up due to oxic conditions in the first few inches of topsoil promoting corrosion), for a buried wiring run; however, your extreme soil conditions are not kind to the notion of needing a 21-22" deep trench to get 18" of cover.  Rigid metal conduit lets you get away with a much shallower trench, 9" deep for 6" of cover in your case, but galvanized conduit, while legal for burial, may not be the wisest thing to bury, depending on soil conditions.  Corrosion-wise, the best choice would be PVC-coated galvanized conduit, but it's a rather expensive beast for a 125' run, especially considering you'll want fat conduit for this job -- I would run 2" conduit, myself, as that leaves enough room for a future upgrade to 200A.  Given the cost of PVC-coated conduit, and the shallow trench depths, I would at least use a polymeric tape wrap designed for corrosionproofing over the conduit as it was being laid in the trench.

In any case, you'll definitely want to rent a mini-excavator with both bucket and breaker attachments for the trenching job -- the former is for digging up soil and broken-up rock, while you can use the latter to break up the limestone bedrock so you can dig it out.  Once the trenching and conduit are done, you'll want to pull 3 1AWG aluminum XHHW-2 conductors for your hots and neutral, and a bare or insulated 8AWG copper ground wire if you aren't using supplemental corrosionproofing on the conduit itself.