Instead of using an inline sinker such as a bullet weight or egg weight you want to use something with a bit of drop to it, either a Slinky style weight (beads sealed in a little nylon bag), a pencil lead, or a cannonball weight off of a dropper. The idea is to keep your bait NEAR the bottom not IN the bottom. The strike zone when drift fishing is in most cases the lower 2 feet of the water column and depending upon species this can vary greatly.
In this image you can see the pencil lead on the left, and the slinky on the right.
Illustrated below is how to rig a dropper setup, most commonly used when fishing Dick Nites, although can be used for any type of drift fishing.
Both of these setups will allow your presentation to be a few inches up out of the rocks, and depending upon how you rig them they will break away leaving your swivel and leader if you get hung up on bottom. You can use surgical tubing as they do in the photo to secure the lead, or do as I do and just punch a hole right through the led and clip it to the snap swivel. Use one end of the barrel portion of the swivel to attach your mainline, and the other end to attach your leader so that the snap hangs down and swings freely in the middle with the attached lead.
The bite when drift fishing can also vary greatly, it is quite likely you are getting bit, but not detecting the strike. When using just a corky and yarn, the bite is often very subtle and may feel like no more than a trout or whitefish pecking at the offering, as a bass fisherman, I am sure you are familiar with identifying the difference between a fishes touch and the bottom, weeds, or a snag. This skill of identifying and classifying bottom inputs vs fish strikes is imperative when drifting as you likely only have a single second (or less) to react to a quick strike before the fish spits your offering.
If you drift with bait such as shrimp, or eggs, the bite is often more noticeable, but not always! Also, when using bait, the fish tend to hold onto the bait much longer, giving you ample time to react. Also, fishing with lures on drift gear such as a dick nite may provide more noticeable strikes, although again they can be quite subtle and often times you will feel your gear STOP drifting rather than any strike, if it stops at any point in the drift SET THE HOOK, its fish on time!
Important aspects of drift fishing:
1) Keep your presentation in contact with the bottom, that's where the strike zone is. You should FEEL your lead "ticking" along bottom every 2-5 seconds. If it is DRAGGING along the bottom continuously you are using too much weight.
2) Don't cast too far upstream, its a recipe for a snag, and you will never feel a strike. Cast to appx 11 o' clock, and allow the gear to swing naturally through the drift.
3) Don't "high stick" your offering. Keep your line at a 45* angle where it enters the water. Less than 45* is ok, but once you start approaching 90* you're high stickin' em. The rod angle is personal preference, just don't hold it straight up in the air.
4) Follow your gear through the drift, don't just stick your rod out there. Cast, mend out the excess line from your cast by either lifting the rod tip, reeling in slightly, or a combination of both. Now follow through on your cast and point directly at your gear. As the gear drifts downstream, follow the line keeping your rod tip lined up with the offering, this way, you will be able to detect to extra subtle strikes, and it is CLEAR if the gear STOPS moving through the drift. Asside from mending your line at the very beginning of the drift you should NOT be reeling during your drift (with the exception of the use of Dick Nites in which case you want to reel SLOWLY as the gear passes in front of you, then stop reeling and allow it to drift naturally from 2 o' clock to the end of the drift).
5) Most of your bites will come at the very end of the drift so don't reel up too soon! Wait for it to go all the way down, and even consider freespooling and paying out a little line at the very end, this often times pays of in numbers! Make sure to cast in a way that your gear gets to the point you think is holding fish at the END of the drift, don't cast to where you think the fish ARE. Let your gear drift naturally INTO the strike zone, do not bomb the fish! You will only be spooking the fish, and frustrating yourself and those around you.
Drift fishing is an art form, and not for everyone. There are TONS of other techniques that are as effective, or more effective in different circumstances. Don't expect to learn overnight, but with patience and persistence it will come to you. The ability to read water and identify where fish will travel/hold is imperative in all aspects of river fishing, learning this skill takes time, but will increase your catch 10 fold.
Good luck.