My typographical knowledge is too limited for me to make a call on whether this is a "good" Bodoni, but affordable it is:

Bodoni Recut FS

Itc Bodoni from Sumner Stone.

Thank you for the suggestions. However, for the ITC Bodoni, it seems that it does not have flat serifs.

What you about URW Bodoni?

What do you mean? The are as flat as can be.

Sorry, when I said flat serifs, I mean straight.

Google "Bodoni font" and inspect the price of what you find, and whether the serifs are sufficiently "flat".

Another approach is to visit the big "department store" online font distributors, which licence fonts from multiple foundries, and search "Bodoni" there, e.g.
MyFonts
FontShop
Fonts.com
Veer

ITC Bodoni 72:

Notice the curved tip of the "b", "l" and "n". This is what I am referring to.

In contrast, notice the serifs of this Bodoni.

URW Bodoni does not have an Italic though, only an Oblique. ITC Bodoni comes in three optical sizes and it suitable for longer text (most Bodonis are not). It al depends if you are looking for a Bodoni for headlines or logos or for running text. Bauer Bodoni is good for headlines, as is Bodoni Antiqua, both from URW, they are very affordable and good quality. ITC Bodoni is more suitable for text (the 6 and 12 pt versions) but the 72 pt version is very nice for display. It is less stiff in its geometry, more elegant, but very nice. Stone Type Foundry has them at a very affordable price.

Otherwise you can search for Didone at MyFonts to get Bodoni-esque fonts

Thank you for the explanations and recommendations. I could not identify the difference between Bodoni and Bodoni Antiqua. Could you help me?

I don't know which bodoni you are referring to. All bodonis go back to the typefaces of gianbattista bodoni. But as he cut various typefaces, for different sizes, there isn't one true bodoni of which others are derivates. Bauer Bodoni is a very classical cut, very good for display use, but a bit too thin and wide for text work, as the thin lines will be very hard to read. Berthold Bodoni is the same as Bodoni Antiqua, it is considered another succesful cut, which is slightly more robust than the Bauer version, so more suitable for text, but still perhaps a bit too refined for that. Then there is ITC bodoni which is actually three bodonis, the 6 is based on gianbattista bodonis small type, the 72 based on his display work, and the 12 is 'generated' as a mixture of the too. overall I would say that ITC Bodoni is a bit more organic than the other too, and more suitable for text work. These are the bodonis I know well, others will differ slightly in their geometry, thick thin contrast, and their detailing (serifs for instance). But these differences seem small at first glance.

I was referring to Berthold Bodoni, Berthold Bodoni Antiqua, URW Bodoni and URW Bodoni Antiqua. I can't notice the difference between them. And once again, thank you for the explanations.

Berenis ADF might fit your specs, too, if all you want is a Bodoni.