In a word, it is a mystery and a supernatural miracle. The miracle of the eucharist and transubstantiation cannot be explained by appealing to the natural laws of nature God has put in the nature of things and the created world. Our faith in the eucharist rests on the words of Jesus who is God, so our faith in the eucharist rests on the word of God. And if Jesus who is God said at the Last Supper ‘This is my Body’ and This is my blood’ then we believe what he said and that he can effect the transubstantiation of the bread and wine into his body and blood by his almighty power just as we believe God created us and the entire world out of nothing. The catholic faith in the eucharist does not rely on human reasoning but on divine revelation.
I don’t believe the Transfiguration or the resurrection of Jesus has anything to do with Jesus being able to transubstantiate the bread and wine into his body and blood. At the Last Supper which was before Jesus’ passion, death, and resurrection, Jesus transubstantiated the bread and wine into his body and blood and gave it to the apostles to eat and drink. So Jesus was both physically present in his body to the eyes of the apostles as well as being physically and substantially present in the consecrated bread and wine he gave to the disciples to eat and drink. Jesus as God had the power to effect the miracle of the eucharist his whole life long. The transfiguration of Jesus is a manifestation of Jesus’ divinity showing through his humanity which he always possessed since his incarnation.
How Jesus without leaving heaven is also under the sacramental species of the bread and wine wherever the eucharist is celebrated, on every altar and in all the tabernacles throughout the world is beyond our knowledge and experience of the world. But, we do not believe it is beyond the power of God to effect this as the Council of Trent decreed:
For neither are these things mutually repugnant,-that our Saviour Himself always sitteth at the right hand of the Father in heaven, according to the natural mode of existing, and that, nevertheless, He be, in many other places, sacramentally present to us in his own substance, by a manner of existing, which, though we can scarcely express it in words, yet can we, by the understanding illuminated by faith, conceive, and we ought most firmly to believe, to be possible unto God ( Decree on the Eucharist, chapter 1).
As far as Jesus’ body and blood in the eucharist being in a place, St Thomas Aquinas teaches that technically speaking the body and blood of Jesus in the eucharist is not in a place: The place and the object placed must be equal, as is clear from the philosopher (Phys. iv - Aristotle). But the place where this sacrament is, is much less than the body of Christ. Therefore Christ’s body is not in this sacrament as in a place. (ST, Pt. III, Q. 76, art. 5). Following St Thomas, The Catechism of the Council of Trent also teaches that our Lord is not in the sacrament as in a place. Besides the Catechism of the Council of Trent, I believe there are only two instances in the Church’s official magisterial teaching from two popes addressing the issue of ‘place’ in reference to Christ in the eucharist. One is from Pope Paul VI in the encyclical MYSTERIUM FIDEI in which he says “once the substance or nature of the bread and wine has been changed into the body and blood of Christ, nothing remains of the bread and the wine except for the species—beneath which Christ is present whole and entire in His physical “reality,” corporeally present, although not in the manner in which bodies are in a place.” The other instance if from a prior pope which I believe I read in one of my books on the eucharist but which I don’t have the time presently to look up. Now, the issue about ‘place’ in reference to Christ’s body in the eucharist I don’t think is dogma but probably belongs to the ordinary teaching of the magisterium. The Church has not said much about this officially but what I have related above.
As far as bi-location, I believe St Thomas Aquinas was not in favor of this explanation. I believe his opinion was that a body in its natural way or form of existing can be only in one place at a time. For example, as the Council of Trent decreed above, the body of Christ is in heaven in its natural extended existence, but the whole body and blood of Christ in the eucharist is under the species of the bread and wine as substance or after the manner of substance. If I’m not mistaken, Blessed Duns Scotus favored a bi-location explanation.