Hi Brian,
That sounds very complicated to do all in one image. ie; why not find a bug in a web outside lit by the morning sun.
For this image, if possible (the bug looks dead) I would suggest putting the bug on a piece of glass over a prettier background.
Spiders webs, glass, and a bug
Basically choose any one of the above and concentrate on that.
There are many options but none are easy. You seem to have the main subject fairly well here, but at the expense of a lot of background noise. But that can be improved with a little editing.
This seems like one of those instances where you were faced with having to use a high Iso plus low shutter speed and too wide an aperture. But the only real alternative is to add extra lighting; and in this case, that might well cause other issues.
So about all that you can do, if you don't have any 'studio type' lighting is to shoot with a longer shutter speed on a tripod, providing there isn't any subject movement. This would enable you to cut your Iso by around a half.
I was in a similar position recently when attempting to photograph fungi in the woods, where flash was giving false colours.
Some exposure compensation is often necessary. In an ideal world, I shoot with aperture priority and a setting around F11 to F16. If using flash, I manually set the camera to something suitable (eg F14 and 1/200 with Iso 200) then apply some flash output compensation as required.
Geoff it seems i am forced down the road of 'manual operation'. Big big shudder and sigh from this newbie.
One trick for better backgrounds that I sometimes use for flowers that are being photographed indoors, or a few other uses. Is to print out a background of leaves, or sky, etc, onto matte paper and use that to create a false background.
It needs to be sufficiently distant, or use an out of focus image, in order to look natural.
Not always suitable but something to consider.