If you get all your Ground Supply as light vehicles, ground force supply costs 2.48 vendarite for 500 GSP. Infantry are cheaper, but I don't know the cost off the top of my head (I found the LV supply costs in screenshots on the original rules posts).
Infantry-based supply is 1.0 vendarite/BP per 500 GSP. LVH logistics used to have an important role as their cost was balanced by the ability to auto-resupply formations in their hierarchy, however since 1.12 and the replacement mechanic it is far more cost-efficient to use only INF+LOG-S organic to every formation as well as organized into rear echelon supply dumps with "Use for Replacement" checked.
HCAP is 12? GSP for 6 shots, so 500 GSP gives us 250 shots. To get 5000 shots (so assuming 20% as accurate as the bombardment) we'd need 10000 GSP. This costs us 49.6 vendarite (and nothing else).
This is incorrect. First off, HCAP is 9 GSP. Second, the GSP listed is the amount required for 10 rounds of fire, not one - so you pay 9 GSP per 60 shots, not 6. In this case to get 5,000 shots you are paying 750 GSP which with infantry logistics comes out to 15 BP/vendarite.
It is also important to emphasize the relative low value of vendarite compared to duranium and gallicite which are used to build MSP. I have never experienced anything even approaching a vendarite shortage, so expending it is not a big deal to me even if the cost is several times more than for the same operation in MSP.
A 10cm, 30000km range railgun costs 14BP and so consumes 14/100/4 MSP per shot. 1 MSP is 0.25 BP. So 1000 railgun shots (which are EXTREMELY cheap as orbital weapons go) costs 2.5BP. This looks like a great deal for the bombardment! Except you had to sit at 30000km to kill the STOs and so you probably lost your entire navy.
You'll want to check your math: (14/100/4 MSP/shot) * (1000 shots) * (0.25 BP/MSP) = 8.75 BP.
A better weapon for killing STOs is a particle beam (since range doesn't affect orbit to surface accuracy, but DOES affect STO accuracy, shooting from farther away favors the attacker). Consider a Strength 6 beam (so plenty to demolish an STO if it hits) with 240,000km range and 15 second cycle time. This costs 94BP, and so consumes 94/100/4 BP per shot. At 1% accuracy, to kill 10 STOs, we'd spend 23.5BP. This is probably still cheaper than killing them with ground troops at equivalent accuracy, but consumes much more valuable minerals (gallicite and duranium instead of vendarite). If you use bigger, badder particle beams the cost goes up. The cost of using ground troops remains constant.
The correct formulation is: (94/100 MSP/shot) * (1000 shots) * (0.25 BP/MSP) = 235 BP. Note that there is no division by 4 as a particle beam fires one shot per weapon firing (compared to the railgun's 4 shots per firing).
Of course, the missile you proposed to use instead cost 200 BP. And you'd need a lot more than one if there are any point defense STOs. So the ground forces kick its butt.
With the ground forces, you also need to consider the expense of building, repairing, and replacing the heavily-armored transports you will need to actually break through the STO screen, drop troops, and escape back out of range. If the planet is heavily defended by enemy ground forces, you will likely need to do several waves of drops to accumulate multi-million tons of ground attackers on the planet surface, further increasing losses. Depending on just how heavily defended the planet is, as well as various factors such as technology, ship design, etc., the expense of dropping ground forces may well exceed that of bombarding from orbit just because of the damage to and/or loss of dropships. This is really the major factor that will make the orbital bombardment approach tend to be the most effective, especially if you have sufficient shield technology to absorb enemy fire at extreme range in which case you will not even have to pay duranium to repair scratched paint on your battleships.