A bull market has finally arrived, giving investors a reason to cheer. That's because these market phases are known for rising share prices, and that generally scores a win for your portfolio. In fact, past bull markets since the mid-1970s each have delivered triple-digit gains, according to data compiled by Raymond James & Associates.

All of that sounds great, but you may be worried about one detail -- and that's finding bargains in a rising market. After all, bull markets are declared only once an index reaches a new all-time high, meaning that, by the time we know we're in a bull market, that market actually has been around for a while. For instance, today's bull market has been going on for about 16 months. As a result, some stocks may have had the time to soar, and in certain cases, to become too expensive.

But here's the good news: Just because many stocks climb in a bull market doesn't mean all of them are overpriced. Some of these players have excellent long-term prospects, so their shares could extend gains well into the future. And some quality stocks haven't yet taken off, offering us a buying opportunity. So, let's go bull market bargain hunting and check out two top growth stocks to buy now.

Two investors smile while looking at something on a computer screen.

Image source: Getty Images.

1. Amazon

Amazon (AMZN 3.43%) climbed 80% last year, and the stock already has advanced another 15% so far this year. That's left Amazon trading at 41x forward earnings estimates, which actually isn't expensive for a company with a solid earnings track record and enormous growth potential ahead.

Amazon is a leader in two high-growth areas: cloud computing and e-commerce. And on top of this, Amazon took steps over the past year or so to improve its cost structure -- efforts that should help boost profit over time.

For example, the company worked to make its fulfillment network more efficient and reduce delivery times. And Amazon favored investing in high growth areas, such as technology infrastructure to support cloud business Amazon Web Services (AWS).

So, Amazon's leadership in cloud and e-commerce, as well as the recent cost efforts, should supercharge growth over the long term.

Finally, Amazon's focus on another high-growth area could boost growth even further. I'm talking about artificial intelligence (AI). Amazon is using AI to improve its e-commerce operations and offer shoppers a great experience. The company uses AI to design the most efficient delivery routes, for example, and to offer shoppers suggestions of what to buy based on their purchasing history.

As for AWS, it offers AI services across all of its clients' needs, from chips to train their own AI models to a fully managed service offering top foundation models for customization.

In the most recent quarter, Amazon's net sales rose 14%, and operating income more than quadrupled to $13 billion thanks to all of these points -- and together, these elements make me confident growth is far from over.

A person smiles while hugging a dog outdoors.

Image source: Getty Images.

2. Chewy

Chewy (CHWY 2.99%) shares have failed to take off even though the online pet supplies retailer has reported quarter after quarter of good news. That's OK. This offers long-term investors a terrific buying opportunity. Today, shares of this top company trade for only 23x times forward earnings estimates, an absolute steal.

Why buy Chewy? First, the company addresses a large, and as Chewy says, "resilient" market, totaling $144 billion in the U.S. Consumers generally prioritize their pets, meaning the market may quickly bounce back after times of economic weakness, and even during these tough times, Chewy has managed to keep growth going.

And this brings me to my second point: Chewy has built up a loyal customer base, and that's reflected in earnings. In the most recent quarter, Chewy's net sales per active customer climbed in the double digits, and total net sales advanced in the high single digits.

What really illustrates Chewy's solid place in customers' lives is numbers from its Autoship program. This is a service that automatically reorders and ships your favorite products right to your door. Autoship now makes up more than 76% of Chewy's total sales. These numbers offer us an indication of future sales, since they are recurrent and make up such an enormous percentage of Chewy's total sales.

At the same time, the company is debt-free and ended the recent quarter with more than $957 million in cash, allowing it to pursue growth goals -- such as the current expansion into Canada.

All of this makes Chewy a fantastic bargain growth buy right now.