As seen in Installing Windows 98 on a Modern Laptop
Download animated LOGO.SYS
(place in C:\LOGO.SYS to set as the Windows 98 boot image)
Download animated 320x400 256-color bitmap
Download original PNG
Windows 98's default startup animation is stored in C:\IO.SYS, but if C:\LOGO.SYS exists, it will override the default and use the logo stored there instead. LOGO.SYS must be a 320x400 256-color bitmap (Microsoft Paint will make compliant ones as long as it's saved as 256-color).
The animation is a little trickier. The Windows 98 logo animation is provided by a cycling a section of the bitmaps palette, so special attention must be paid towards the placement of colors in the palette, and then the bitmap header must be hex edited to specify the range of the palette cycle. This is a non-standard usage of the bitmap header and therefore this image will not animate in any conventional image viewer, only when used in Windows 98's boot process.
The LOGO.SYS and 256-color bitmap provided above are actually the same exact file just with a different filename, the bitmap provided for convenience. They both have been hex edited to palette swap correctly in Windows 98's boot process. The high quality PNG has no loading bar and cannot be directly converted to an animated bitmap anyway without palette/hex editing.