Yes, there is a bullish bias in the 'stock market', but it's mostly do to survivorship bias. The strong get stronger and the weak eventually go away.
I don't recall the numbers precisely, but I believe only 14 of the 30 present Dow Industrials members were present in the index in 1985 (taking into account mergers, etc.). That's a greater than 50% turnover, in one of the most sacred of indices. It would make an interesting study to see what level the Dow would be at with the 1985 members.
Good luck to all.