I did a quick count - using 1999 as a basis year for his home runs, and identifying two outlying batting average years (2002 and 2004) my estimate is that Bonds without steroids likely would have ended up with 679 lifetime home runs, and with a career batting average maybe 3 points lower - say .295. In other words, his lifetime record without the effect of steroids would likely have been almost exactly the same as the career numbers of Willie Mays, a few points higher and a few home runs more, though Mays was the better fielder.
So we would still have Bonds in the top 5 and a contender at least for number 2 all-time, and maybe even for number 1 all-time without the effects of steroids.
How did I calculate this? I am not making any pretensions to science here. I note that like nearly every single player ever (see copious writings on this subject by Bill James) Bonds peaked at age -27-28-29 (most do at age 27, though James has noticed that superstars often peak at either 26 or 28 as well), His home run totals go from his greatest pre-steroids year, 1993, and proportionally, in the strike-shortened year of 1994 he may very well have hit more than 50. But I am not correcting for the strike, anymore than for Mantle's injuries, Ruth's years pitching and playing in the deadball era etc. since these were all real, historical events.
Bonds then hit between 33 and 42 homers every year from 1995 to 1999, with 34 in 1999, down from 37 the year before. Let's figure he hits an average of 35 a year over the five years - 2000-2004 in which his numbers are anomalously high for his previous career figures and for his age. I think this is a reasonable estimate based on the idea that Bonds kept himself in good condition, overcame the common decay in batting skills at that age, which is not unheard of for superstars, but did not reach the absurd numbers of 45-49 homers for four of those years nor the statistically insane number of 73 in 2001.
His two especially high batting averages - need to be adjusted also, though this is trickier. In 1999, he hit .262. His previous high batting average was in his best pre-steroid season of 1993, when he hit .336. Instead he hit .370 at age 37 and .362 at age 39. Granted, he showed a degree of discipline that was unbelievable at that age, and this can be partly chalked up to experience and intelligence as a hitter. Ted Williams did hit .388 at age 38, so it is not impossible that these averages reflect some skills that had nothing to do with steroids use. However, steroid use may have given Bonds the confidence that he could get his bat around on the ball even when he waited for his pitch - Williams hit 38 homers that year near the end of his career, his career high was 43 home runs at age 30 - and the steroids enabling his home run production also meant pitchers pitched him more carefully, which may mean he could wait for a strike. Estimating the effects of all these factors are beyond my skills by far, but I am going to suggest that the two high BA years, since they took place in the same years as the high home run totals due in considerable part to steroids, were partly the result of this use, since a few of those home runs might have been caught on the warning track minus steroids, and so his BA was higher, should be downgraded a bit, though unsure how much I will suggest a 2-3 point effect on his lifetime average and not more, which I think would be over-estimating the likely effect, so a BA around .295 instead of .298 for his career.
.298 679 home runs, we are so close to Willie Mays' career numbers ! Mays missed some time in the military - most of 1952, his second season and all of 1953. He had hit 20 home runs in his rookie year and hit 41 when he came back in 1954. So figuring that Mays should have had another 55 home runs, and would have broken Ruth's career record just a couple of years before Aaron did is not unreasonable. If we give Mays 55, give Bond 55 for the year 1994 (he had 37 in 112 games) we would have Mays 716, Ruth 714, Bonds 679 plus an additional 18 for the strike year games missed = 697. Hard not to argue that Mays and Bonds are essentially equals as players.
Babe Ruth pitched in 17 games in 1919, and hit 29 home runs playing in the outfield or in those games he pitched. He played 130 altogether. His playing primarily in the OF coincided with the use of the "jack rabbit" ball, so it is hard to estimate Babe Ruth home runs if he had not been a pitcher. He played in 95 games in 1918 and hit 11 home runs. So 15 home runs a year is a conservative estimate but if we went with that as our estimate for 1914 to 1917 his total for those seasons would go from 9 overall to 60 for those four years. This seems excessive though. Ruth was a rookie in 1914 and played in only 5 games (as a pitcher of course). So that method won't work.
How about if we figure out his home runs per PA for 1915-1917? Ruth was up to bat 397 times in those years and hit 9 homers - one every 44 PA. If we assumed that he played OF for 440 PA a season for those three years and hit one homer for every 44 PA, his total for 1915-1917 would be 10 per year or 30, adding 21 home runs to hit lifetime total of 714 to reach 735.
As for Ted Williams, who lost three full seasons during WWII and 1 4/5 seasons in 1951-2 during the Korean War, we could adjust as follows: Wiliams hit 367, 36 and 38 homers respectively in 1940, 41 and 46, the two years before he entered military service and the one when he came back. Plus he was 27 in 1946, when most players peak, so it is not an unreasonable estimate. So let's give him that average of 37 homers for each of 1942-44 and so we add 101 home runs to his career total. He hit 28 homers in 1950, 30 in 1951 and 29 in 1954, again very conveniently giving us an easy benchmark for the two seasons before entering the Korean War service and the one immediately following. He missed all of 1952, and in 1953 had 13 home runs in 110 PA (on track in theory for a 70 homer season but these kinds of streaks happen frequently). If we again give him the average of 29 for 1952 and figure that with that great power start in 1953 he does better and hits 35 overall we add another 22 for that season and 29 for 1952 so another 51. That would give Williams 152 additional home runs over his career for a total of 673.
I don't find any similar adjustments needed for Henry Aaron, who entered MLB at age 20, granted having played in the Negro Leagues before that, but having a pretty normal very good rookie season at a young age - .280 13 homers.
Last adjustment is of course for A-Rod. In 1998, 99 and 2000 he hit 42, 42 and 41 home runs. Let's give him 42 for 2001-2003 when his numbers are over the top, reducing his total by 30. Then he hits 36 in 2004 and 36 in 2006 and 35 in 2008. Let's reduce the two statistically anomalous years - 2005 and 2007 to 36 and we get another 30 off his career total, giving A-Rod 627 for his career.
If these admittedly crude estimates were to be right, and if history had taken these turns, the all time home run list would look like this:
Henry Aaron 755
Babe Ruth 735
Willie Mays 716
Barry Bond 697
Ted Williams 673
Ken Griffey Jr. 630
Alex Rodriguez 627