The best replacement for bicubic is bilinear.

The best alternatives to bicubic are rated as following:
★★★★★  bilinear
★★★★  bilinear interpolation
★★★  average downsampling
★★★  nearest neighbor
★★★  lanczos
★★  bicubic smoother
★★  bilinear photoshop
★  lanczos3
★  subsampling
★  bicubic sharper
★  lanczos 3
  bilinear better
  genuine fractals

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bicubic
bilinear
bilinear interpolation