Here is what Pete says about rubbing and sanding his bats on pages 78-80 of his 1985 book with Peter Golenbock titled "Pete Rose On Hitting."

Note: The book's many illustrative photographs show Rose wearing his Reds home uniform and wielding a Mizuno PR4000 model ash-colored bat -- so the photos were likely snapped after August 17, 1984 and before the start of the 1985 season.

"Making Adjustments
Every night after the game, I take a clean towel and some alcohol, and I clean off the barrel of my bat. Some of my teammates think I'm crazy. Let me explain why I do it.
It is crucial to me that I begin the game hitting with a clean bat. Ninety-nine times out of a hundred when I hit the ball, it leaves a mark on the bat, so that starting with my first time up, I can come back to the dugout and actually study my bat to see whether I was judging the speed of the pitches properly.
My goal is to hit the ball at the signature on the bat. That tells me I am meeting the ball squarely.
Say I am leading off and a pitcher throws a fastball, and I foul it back. If I look at the bat and see a mark down near the trademark, I'll say to myself, "This guy is throwing harder that I thought he was." Because I wasn't quick enough, I didn't get the bat out fast enough to hit the ball at the signature. If I hit it up near the end, I'll say, "He isn't throwing all that hard." I swung too quickly. I should have waited longer.
If the mark is right where it's supposed to be, I say to myself, "I'm right on the guy. There's no problem." I know I have him.
By the end of the game, I've noted every single one of the marks on my bat and understood how they got there.
Many times during the course of a game I will check the marks on the bat and make an adjustment. Sometimes in the middle of the count, I'll foul the ball off, look at the bat, and adjust my hands either up or down the bat for the next pitch.
I remember I was facing Craig Swan during my forty-four game hitting streak. I had reached thirty-eight games in a row. The first pitch of the game was a ball. Then Swan threw an inside fastball, and I fouled it back. I called time out and looked at the bat. The mark was about an inch down the handle from where it should have been. He was throwing harder than I had thought. So I choked up a little, trying to make the bat a little lighter.
Swan again threw the same pitch inside, but this time I hit a line drive over the shortstop's head for a base hit. If I hadn't adjusted, it would have been another foul ball, and the count would have been 0 and 2.
I clean my bat after every game to prepare it for the next game. If the bat is chipped, I sand it down to keep it smooth. I use the same bat so many times that after a couple weeks, my name "Genuine Pete Rose Mizuno" wears off completely.
It doesn't take any time to clean the bat off. Why don't other players do this? I don't know. Maybe they think it's too much trouble.
Some players will check their bats to see where they've been hitting during batting practice. By they don't do it during an actual game when it's more valuable.
I make adjustments in two of my four at bats. To me it's all part of the fun of the game, of being involved in the game. And the adjustments make me concentrate on my one goal: hitting the ball hard.
I have been cleaning my bat for so long it has become a ritual. When I come in after the game, the first thing I will do is sit down and clean the pine tar off my batting glove with the alchohol. I put alcohol on my towel, clean the glove off, put the glove up and then use the towel to wipe off my bat.
After I do that, I remove the strip of tape toward the handle of the bat. That strip of tape has my pine tar, which keeps the bat from slipping. The tape keeps the pine tar from caking up on the bat. When it gets too heavy, I remove the tape and put on a new strip."