First, carefully inspect the injury. If there are punctures that penetrate into the fat, consider the possibility that there is gravel under the skin.
Check the stability of any areas of deeper skin injury by stretching the edges. Decide whether this will be a permanent dressing, or just a temporary patch until you get to the doctor.
It's easiest to scrub immediately after the injury. A couple of hours later, the wound will be more sensitive.
If you need a "scrub brush," the seam of your biking shirt sleeve can help remove stubborn dirt. A benzalkonium chloride towelette is a good antiseptic cleaning tool. Wrinkle it up, so the edges can remove dirt.
If you're on a short ride and the wound isn't bleeding, you could defer thorough cleaning until you're in the shower. A few minutes in the water will soften up the blood and dirt. The warm water tends to numb up abrasions and lacerations, so they're easier to clean. Then take a rough washcloth and scrub the hell out of those scrapes. They need to be pink -- no brown dirt color remaining!
The antibiotic ointment protects the wound from dryness. It helps keep the bandage from sticking to your wound. And of course, it kills germs to reduce the infection risk.
Even if the bandage is only temporary, the antibiotic ointment can help dissolve road tar and soften any remaining dirt, so it will be easier to clean later.
Place a non-stick pad over the wound. It should be large enough that it can slide or shift a bit without uncovering the wound. Telfa and Adaptic are sample brands.
If additional padding is needed, put gauze pads over the non-stick pad to provide thickness, or use a padded roll gauze (sample brand Kerlix) to cushion the area.
If the injury is over an area that will move, such as the elbow or knee, apply the gauze while the joint is half-way bent (about 45 degrees off of straight). To keep the dressing from creeping as the joint is moved, be sure to wrap the full width of the roll gauze circularly above the joint and below the joint.
Tape can be used to hold the dressing, but doesn't provide dust and moisture protection like Coban. And it tends to pull loose as you continue biking. I almost never use any tape in dressings, because it just doesn't work very well.
If you're not absolutely certain the wound is clean, it will need a "re-do" when you get back. Decide whether you're heading for the doctor, or taking care of the wound yourself.
If you're planning home-care of a wound that remains dirty, hit the shower. Scrub the wound mercilessly with an abrasive sponge or washcloth. Expect to make it bleed again, but be sure you've gotten it clean. Then redress it with fresh material.