The literal translation is: "per favore, potresti portarmi la mia borsa?", but however bear in mind that in Italian we don't use the possessives so frequently as they are used in English when talking about personal belongings. For instance, if it's implied, that is it's already known by the listener, that the bag is mine, I wouldn't use the possessive, while in English I think you would use them in any case. Even if the listener knows that the bag is yours, I think in English you would say: "could you bring me my bag, please?", while in Italian we would just say: "per favore, potresti portarmi la borsa?".

Ciao. As said before, the correct answer is "per favore, potresti portarmi la mia borsa?". Alternatively, you can also say "per favore, mi potresti portare la mia borsa?". Then, if you want, you can move "per favore" at the end and say "mi potresti portare la mia borsa, per favore?", or "potresti portarmi la mia borsa, per favore?". "Prendere" can be translated as "to take", like in this example: Prendi la mia borsa e portala qui. = Take my bag and bring it here. I hope this is helpful.

Slightly inaccurate. "Per favore, potresti portarmi la mia borsa?" PortarMI = Bring ME