The best replacement for bilinear is bicubic.

The best alternatives to bilinear are rated as following:
★★★★★  bicubic
★★  anisotropic
★★  trilinear filtering
★★  trilinear
★  nearest neighbor
★  lanczos
★  bicubic resize
★  cubic convolution
  bicubic photoshop
  nearest neighbour

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bilinear
bicubic
anisotropic