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.
Skills is so important in trading since whatever season it comes, we can maximize the opportunity shows each season we encounter and it takes a lot of effort then also time before we can be in situation where we became a good trader.
Much better we should forget about seasons since we can make a basis on what might be the next scenario will came and then we can plan our next action with it. To many opportunities what bearish and bullish season can bring it just we need to be skilled enough to spot it.