Womens sportswear:Sports Bra's for cycling and triathlon. ShockAbsorber, Champion, Insport, Sugoi. A good quality sports bra is essential for cycling and triathlon. For triathlon the bra must be supportive enough for the run and dry quickly for a comfortable bike and run following the swim. Look for a bra made from a single layer of fabric - we note this in the "Girls say" comment, to help you.