Is surface rust something to be worried about?

[Gamerancher]

I always have an old hand towel very handy when cleaning. Wiping any fluids off your hands straight away prevents transfer to any parts of your rifle you don't want it on.
Also wiping your cleaning rod dry after each use with solvents prevents contamination and watch where you put it down. Just putting it straight on a concrete bench will pick up small dirt particles which are abrasive to your bore. Keep it dry and keep it clean.

[Tiger650]

I once had a factory standard issue .308 Remington [carbon steel] varmint weight rifle that shot .060" 5 rd groups @ 200 yds, you could head shoot a mouse at 200 yds LOL.

I always patched it through at least once with Sweets every three groups, followed by a metho patch.

The first Sweets patches came out really blue, the rifle obviously copper fouled significantly but was a tack driver [for an off the shelf rifle].

I was relatively poor at the time so never shot it without cleaning to the extent that accuracy may have been effected, being anxious about possible bore damage.

[Tiger650]

PS good advice Gamerancher, a concrete benchtop is made out of sand and one grain of silica in the bore could see accuracy suffer.
Manufacturers of abrasives swear by the stuff.