As far as code goes, I think you're okay with your approaches since you've tagged hots appropriately.
Personally, I think mixing cable with individual wires is sloppy. I'm going to assume that 12 AWG is the correct size for the pump, but you should check before actually putting in 12 AWG. I would do one of two things:
Run using NM cable:
- A 12/2 wire for the 240V pump circuit: either black/red, or black/white tagged as hot
- A 14/2 wire for the 120V alarm circuit
- Ground in both cables is connected
Or run individual wires:
- 2 12AWG's (black/red) for the pump circuit
- 1 12AWG or 10AWG ground (bare, or green)
- 1 14AWG white neutral (alarm circuit)
- 1 14AWG other color (blue is often the 4th color used) hot for the alarm circuit
NM wire is usually easier to find, and you may even have some already (if not, having spare 14/2 available is never bad). For individual wires you often have to buy a spool of each color which makes going that way for one project more expensive, though you may be able to buy by-the-foot.
In either scenario, labelling everything at both ends is important.
Without being able to see the cables as they enter the cabinet; or the ability to touch or trace them, here is what I assume is going on.
Definitions:
Grounded (neutral) from the service
A typical single split phase service is made up of 3 wires. Two ungrounded (hot) conductors, and one grounded (neutral) conductor. The ungrounded (hot) conductors will connect to the main service panel through a disconnect (usually a large breaker), while the grounded (neutral) connects to the neutral lug. The neutral lug will be bonded (electrically connected) to the neutral bus bar, and all grounded (neutral) branch circuit conductors will terminate at the neutral bus.
Grounding Electrode Conductor
This conductor is used to connect the grounding electrode (ground rod, etc.), to the grounding bus in the panel. All equipment grounding conductors will be connected to this bus.
Bonding Jumper
The bonding jumper is used to bond (electrically connect), the un-energized metal parts of the panel to the grounding system.
Assumption:
Since it appears that (what I assume is) the grounding electrode conductor terminates at the neutral bus, I'm also assuming that this is the main service disconnect. This leads me to believe that the neutral and grounding buses are bonded (electrically connected). In which case, technically, grounded (neutral) branch circuit conductors can terminate at the grounding bus.
So you have two options:
Terminate the grounded (neutral) from the new circuit to the grounding bus.
Move the green wire that is terminated on the neutral bus, to the grounding bus. Then terminate the grounded (neutral) from the new circuit, to the freed up slot on the neutral bus.
Additional Information and Code Compliance:
Number of Conductors
Since this is a new circuit, it has to be installed to current code standards.
National Electrical Code 2011
ARTICLE 250 — GROUNDING AND BONDING
VI. Equipment Grounding and Equipment Grounding Conductors
250.140 Frames of Ranges and Clothes Dryers. Frames of electric ranges, wall-mounted ovens, counter-mounted cooking units, clothes dryers, and outlet or junction boxes that are part of the circuit for these appliances shall be connected to the equipment grounding conductor in the manner specified by 250.134 or 250.138.
Which in this case means installing a NEMA 14 receptacle for the dryer, and a proper grounding conductor.
You'll have to follow the dryer manufacturers installation instructions for upgrading to a 4 wire cord. For more information see this answer, and this answer.
Since you've said that you're already using 4 wire cable, you'll simply have to terminate the grounding conductor in the cable to the grounding bus in the service panel. Then connect the other end of the grounding conductor to the grounding terminal in the dryer receptacle.
Size of Conductors
You'll also want to be sure that you're using the proper size breaker and conductors. In the case of a dryer, you'll typically use a 30 ampere breaker and 10 AWG conductors (depending on the length of the run). However, you'll want to check the dryer manufacturers installation instructions to verify this.
Best Answer
The only sure way to hunt down missing wires, without taking forever, without disturbing the walls, ceiling, or floor is to use a circuit tracer. I use a Mastech MS6818. It comes with a transmitter and a tracer and can be used on energized and unenergized circuits. It may be worth a homeowner to have one if he owns a house like yours and you are determined to track everything down. You might find a local contractor who also has and uses such a device, but I wouldn't let him in unless he has one in his hand when he comes to the door.
If all of that is too expensive your only other option is to verify that it is not a switch leg or some such and doesn't go anywhere. Then just wire nut it off and leave it in the box, then at least keep a mental note as to where it is in case you find something not working.
Good luck and stay safe.