As they say plus Je te fais + verbe i make you Je te fais pleurer, I make you cry. Je te fais un vélo est une expression qui veut dire faire toute une histoire. :))

Je te fait un vélo has the meaning of "je t'offre un vélo" = I offer you a bike, and hence: je te fais un vélo en cadeau "en cadeau" had been deleted because the meaning is obvious so no need to add it as an emphasis basically other example: je te fais un prix = I'll make you a price (when bargaining) je te fais un bisous = I'll give you a kiss je te fais une offre = I'll make you an offer

it's not straightly , it's literally ... we can not compare sometimes French with English. Je te fais , is from the verb (Faire) , faire quelque chose , does not mean give , but mean do , and do something to someone , it can be giving him something , or helping him , ....etc Je te fais un vélo , if you replace 'fais' with another verb for example 'offre' it will be Je t'offre un vélo , i offer you a bike , and now it seems clear i think !