Hi Erik,
My point doesn't concern the wire color. bonsaiAl1 can vouch for me having no taste about wire color and using "
dazzle wire" on occasion
When copper wire is used for bonsai, it is annealed (a heat treatment) that allows it to go on butter soft and then harden up after it is bent. The wire you are using is bright copper (or appears to be so). The lack of surface oxidation means that it is not annealed, so it goes on hard, and you won't see much holding power for a given thickness. Until you've tried using an annealed wire none of this will make any sense.
Nevertheless, you will find it much more effective to use a larger gauge of wire (preferably annealed copper or anodized aluminum) and apply it at approximate 45 degree angle for maximum holding power. There is more info on this in the FAQ entry listed earlier. Simply wrapping wire on the trunk at nearly parallel winds won't do anything functional, particularly at a gauge this small.
If you find it difficult to work with larger wire gauges, some beginners find it easier to start out with aluminum wire, which has less holding power for the same size, but it is much more forgiving. The aluminum wire for bonsai has been anodized with a coppery color so it isn't as visually obtrusive as it might otherwise be.
Hope this helps,
Matt