Warren Buffett is known for his stock-picking strengths, which have led to spectacular market performance over the long term. Buffett, as Berkshire Hathaway chairman, and his team have delivered compounded annual gains of more than 19% over the past 57 years. That's compared to a 9.9% increase for the S&P 500 index. So when you follow Buffett into a stock, you generally can do it with confidence.

With markets rallying this month and building on this year's gain, you might want to follow the billionaire investor into stocks that could excel in a bull market. We haven't yet reached that market phase, but we're heading there, and now is the perfect time to stock up on a few growth players.

And Buffett just so happens to own two that could roar higher in the next bull market. Let's take a look at each.

1. Amazon

The e-commerce and cloud computing markets are growing in the double digits, and Amazon (AMZN -0.66%), thanks to its leadership in both, is set to benefit. The company has grown earnings over time in both areas, only halted temporarily last year amid rising inflation and economic weakness.

Importantly, Amazon used that slowdown as a time to improve its cost structure not only to face current headwinds but also to strengthen its ability to grow over the long haul.

The company focused on improving efficiency and made a big step when it shifted its U.S. fulfillment network to a regional system from a national one. This allows Amazon to keep inventory in several centers around the country, reducing delivery distance. As a result, deliveries become faster, pleasing the customer, as well as cheaper, pleasing Amazon.

The company also has been investing in key growth areas such as artificial intelligence (AI). This technology is playing a big role in Amazon's e-commerce and cloud computing businesses, meaning it could boost earnings well into the future. Amazon uses AI to streamline its e-commerce operations, for example, predicting popular items to stock, and it offers AI tools to customers through Amazon Web Services (AWS), its cloud business.

Amazon's efforts already are bearing fruit, with the company reporting growth in revenue, net income, free cash flow, and other key metrics in the recent quarter. It's clear this could become a lasting trend as Amazon continues to improve efficiency and the economic situation improves -- and this sustained growth could make Amazon a winner in the next bull market.

2. Apple

Warren Buffett is known for his love of companies with moats, or strong competitive advantages, and this may be why Apple (AAPL 0.07%) makes up such a big share of his portfolio. The maker of products such as the iPhone and Mac has a solid base of fans who won't switch to other brands and are even ready to pay higher prices.

This offers us reason to be confident about Apple's product revenue over time. Of course, there may be moments -- such as recently -- when negative currency impact or a difficult comparison quarter (in this case, for Mac and iPad) weigh on growth. But these situations are temporary and don't reflect a lack of demand for Apple's products.

In the recent quarter, iPhone sales reached a September quarter record, and the installed base reached an all-time high. The installed base of Macs also attained its highest level ever. And half of Mac and iPad buyers were new to those products. So, Apple not only has been able to keep its customers loyal, but it's also still growing its customer base.

Meanwhile, the company's services business has taken off, with revenues there reaching a record, and this unit could be a significant revenue driver from this point forward. By services, I mean a broad selection of subscriptions product users can sign up for -- from digital content to cloud storage. Another positive point is that services are high margin -- with a gross margin of more than 70% in the recent quarter -- meaning they are highly profitable for Apple.

So Apple is on the right track to extend its track record of growth and is in the perfect position to roar higher in a new bull market.