So, I was testing some texturing and of course wanted to test the mipmapping possibilities. Here I tripped over some “problems” you have to avoid by going another way.
In a probably classical way you could use glu to build the mipmaps

gluBuild2DMipmaps(GL_TEXTURE_2D, 3, sizeX, sizeY, GL_RGB, GL_UNSIGNED_BYTE, data);

You hand it the width and height and the texture data and it creates all your needed mipmaps. Problem solved! Unfortunately Android only provides a very small GLU implementation with some helper functions and does not provide you that functionality. Therefore, you would have to go another way.
A possibility on an Android system could be to test for version 1.1 of your GL and use the according hint, as 1.1. adds automatic mipmap generation

gl.glBindTexture(GL10.GL_TEXTURE_2D, textureID);
gl.glTexParameterf(GL10.GL_TEXTURE_2D, GL10.GL_TEXTURE_MAG_FILTER, GL10.GL_LINEAR);
gl.glTexParameterf(GL10.GL_TEXTURE_2D, GL10.GL_TEXTURE_MIN_FILTER, GL10.GL_LINEAR_MIPMAP_NEAREST);
if(gl instanceof GL11) {
  gl.glTexParameterf(GL11.GL_TEXTURE_2D, GL11.GL_GENERATE_MIPMAP, GL11.GL_TRUE);
  GLUtils.texImage2D(GL10.GL_TEXTURE_2D, 0, bitmap, 0);
} else {
  buildMipmap(gl, bitmap);
}

For the emulator this might work but not every mobile device running Android must have a GL11 instance. Therefore, this solution can work but does not necessarily have to.
Mike Miller had a similar problem/idea and suggested the following functionality

private void buildMipmap(GL10 gl, Bitmap bitmap) {
  //
  int level = 0;
  //
  int height = bitmap.getHeight();
  int width = bitmap.getWidth();

  //
  int[] textures = new int[1];
  gl.glGenTextures(1, textures, 0);
  textureID = textures[0];

  //
  gl.glBindTexture(GL10.GL_TEXTURE_2D, textureId);

  //
  while(height >= 1 || width >= 1) {
    //First of all, generate the texture from our bitmap and set it to the according level
    GLUtils.texImage2D(GL10.GL_TEXTURE_2D, level, bitmap, 0);

    //
    if(height == 1 || width == 1) {
      break;
    }

    //Increase the mipmap level
    level++;

    //
    height /= 2;
    width /= 2;
    Bitmap bitmap2 = Bitmap.createScaledBitmap(bitmap, width, height, true);

    //Clean up
    bitmap.recycle();
    bitmap = bitmap2;
  }

  return textureID;
}

The code is pretty straight forward. It just creates always the mottled bitmap and adds it using GLUtils to the according level, beginning from 0 to whatever level the size 1 for width or height will be.
Unfortunately again, this did not work for me. I tried this in an existing code I had, a special plain project just for mipmap testing, with different AVDs and with different circumstances. Nothing worked! As soon as I added another layer the texture stayed white. I am aware that as soon as you set the texture parameters for mipmapping

gl.glTexParameterf(GL10.GL_TEXTURE_2D, GL10.GL_TEXTURE_MAG_FILTER, GL10.GL_LINEAR);
gl.glTexParameterf(GL10.GL_TEXTURE_2D, GL10.GL_TEXTURE_MIN_FILTER, GL10.GL_LINEAR_MIPMAP_NEAREST);

it wants all layers. The function posted by Mike provides these but still it did not work for me. I had no idea why it did not work, because that it is a common solution, trivial and eventually should work. (Nevertheless, I solved it. Read at the end of this post why it did not work for me.)
I do not remember why I tried the following, but after many hours and lost hair I replaced the line of GLUtils.texImage2D(GL10.GL_TEXTURE_2D, level, bmp, 0); with the following, actually resembling what GLUUtils should provide, but based on an older SDK version

ByteBuffer bytebuf = ByteBuffer.allocateDirect(bmp.getHeight() * bmp.getWidth() * 4);
bytebuf.order(ByteOrder.nativeOrder());
IntBuffer pixelbuf = bytebuf.asIntBuffer();

for(int y = 0; y < bmp.getHeight(); y++)
  for(int x = 0; x < bmp.getWidth(); x++) {
    pixelbuf.put(bmp.getPixel(x, y));
  }
pixelbuf.position(0);
bytebuf.position(0);

gl.glTexImage2D(GL10.GL_TEXTURE_2D, level, GL10.GL_RGBA, bmp.getWidth(), bmp.getHeight(), 0, GL10.GL_RGBA, GL10.GL_UNSIGNED_BYTE, pixelbuf);

This basic self-implementation of what should be done by GLUtils works for me. But please note that it is just a working example and does is neither optimized nor necessarily the finite solution to this task.

I also figured out why the GLUtils did not work for me: It was only in the Emulator and it was only on one of my machines. And especially that machine it did not work on has a very basic, cheap, old graphics card. But for a whole overview and if you step into the same trap, I posted everything so you know what could be a reason and how to solve it.

So, now after all these tests I have done I have three implementations that work for me. On the one hand side, the use of GL11 and the self-implementation of a mipmap building method in two ways. In conclusion after all these tests and also minor performance tests I did, use one of the suggested methods from above or let me know of other possibilities. I would start with the GL11 test and then go over to the implementations. GLUtils should always work. Hope this helps…