first, it doesn't matter even if you are more interested in altcoins but most of your portfolio should be bitcoin because bitcoin is the most popular crypto and lowest risk investment. related to tokens that are on the ERC20 network has nothing to do with bullishness because what causes high gas fees is not bullish or bearish but the density of transactions on the network.
it cant be denied that bullish will definitely affect the gas fee, you should've already figured out that there is some real correlation between the increase in gas fee
whenever there's bullish because in bullish the density of transaction as you said is getting higher and higher.
if you're veteran holders, you definitely know back then when NFT was massive added with some blockchain gaming, the fee was becoming so high, more than when the market isn't even in a bullish.
I'd say the market trend, have massive influence towards the gas fee.