First of all congratulations on having a breast augmentation. I hope you have had a great experience in the process and are pleased with everything. There is no minimum time to tan. In order for scars to heal well you need to keep them out of the sun/tanning beds for a year. Therefore, keep lots of sunscreen on your incisions during any UV exposure for a full year. Best wishes
yNot only can your scar be permanently hyperpigmented, you can burn your breast skin, cause wrinkling of your skin at an earlier age and risk getting skin cancer. Self tanning lotions may be safer.,