It all depends on how good you are because there are traders that make more during the bear and the same goes for some that do it better in the bull run.
But if I'll speak for myself, I'd say that it's during the bull run. Because it's like easy to predict what will happen as most of the coins in the market are going to be up thanks to the bull season.
You are right. If someone has good skills in trading, he can get profits both in bearish and bullish seasons. The chance for profits can come at any time, it doesn't depend on the season. However, since the prices tend to drop during the bearish season, the chance for profits isn't as many as in the bullish season. So, it is true that we are easier to predict the price pump/increase during the bullish season than in the bearish season. That's why many people become more active to trade in the bullrun season.
And that's why during the bull season we see these so-called "influencers" and good traders because it's too easy to make a profit during that time.
But come and ask them during the bear market, they'll be gone and they will have a hard time making money during that season. So, those that make good trades during the bear and bull seasons, really are the great traders that are silent and they don't care about other people because they're all focused on their trades and how they make money during these seasons.