Bleeding is a common problem with atlassing as you use higher mipmap levels. But without seeing what you're working on, there's no answer to this. It's all a matter of balance with the specific assets.
You can switch to non-Atlassed textures, or you could add more edge padding. Or you could add a step to your mipmap processing to desaturate them near the edges as you LOD out (so there's less colour bleed).
Depending on how the textures are positioned in your atlas, try setting the wrap mode to clamp instead of repeat. This can fix a lot of bleeding issues from mipmaps sometimes.
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You can switch to non-Atlassed textures, or you could add more edge padding. Or you could add a step to your mipmap processing to desaturate them near the edges as you LOD out (so there's less colour bleed).