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:
![Labeled Image](https://i.stack.imgur.com/SEaES.jpg)
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.
![NEMA 14-30R](https://i.stack.imgur.com/jO6wJm.jpg)
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.
You'd have to look at the old receptacle to be sure. If it's a NEMA 10-50, then the following is true: it is being fed by common 6/2 grounded cable.
NEMA 10 is an obsolete and somewhat dangerous receptacle family, used in the old days for ranges and dryers. It provides hot, hot and neutral - 240V hot-to-hot, and 120V hot-to-neutral. It does not provide ground.
Often, this was installed using the common "/2" cable. There's no choice to color; it's always black, white and bare. In this usage, the white is not a neutral; it's the other hot. The bare wire is the neutral. Really.
Today, a white wire used as a "hot" must be marked with tape. Back in the old days, that was not required if the usage was obvious.
I would make the argument that the old circuit is "grandfathered", which it is. If the 10-50 receptacle broke, you could change it without breaking the grandfathering; in fact the stores sell 10-50R's for only that purpose. I would argue the same is true for changing it to a modern 4-prong NEMA 14-50. I would then use the NEC 2014 rules which allow retrofitting a true ground. Can't promise you the inspector would agree.
Best Answer
If your oven has a white neutral on its connection block, you must connect it. Follow the instructions. Some of these ranges and ovens (maybe all or the vast preponderance) use 240 V for the main heating elements, but 120 V for controls, lights, and maybe even for smaller heating elements. Hence, a white neutral must be connected.
The admonition to not fuse the neutral does not mean a neutral is not needed. The neutral is connected to the neutral bar in the panel and is not fused there. The reason to not fuse the neutral is to never have a loss of the neutral without the loss of both hots. Loss of neutral can lead to the neutral becoming hot (shock hazard) and could lead to loss of control of the oven.