What you state seems to largely reflect the claims made by the Catholic Encyclopedia, which states:

Bruno was not condemned for his defence of the Copernican system of astronomy, nor for his doctrine of the plurality of inhabited worlds, but for his theological errors, among which were the following: that Christ was not God but merely an unusually skilful magician, that the Holy Ghost is the soul of the world, that the Devil will be saved, etc.

However, Wikipedia cites Luigi Firpo as including among the reasons for Bruno's condemnation and execution:

Claiming the existence of a plurality of worlds and their eternity.

I tracked down what appears to be the original book - pdf - by Firpo, which lists:

I. Negare la transustanziazione (accusa [4]). II. Mettere in dubbio la verginità di Maria (accusa [8]). III. Aver soggiornato in paesi d’eretici vivendo alla loro guisa (accusa [10]). IV. Aver scritto contro il Papa lo Spaccio della Bestia trionfante2. V. Sostenere l’esistenza di mondi innumerevoli ed eterni (accusa [5]). VI. Asserire la metempsicosi e la possibilità che un’anima sola informi due corpi (accusa [6]). VII. Ritenere la magia buona e lecita (accusa [7]). VIII. Identificare lo Spirito Santo con l’anima del mondo (censura i). IX. Affermare che Mosè simulò i suoi miracoli e inventò la Legge (accusa [14]). X. Dichiarare che la S. Scrittura non è che un sogno3. XI. Ritenere che perfino i demoni si salveranno (accusa [12]). XII. Opinare l’esistenza dei preadamiti (censura l). XIII. Asserire che Cristo non è Dio, ma ingannatore e mago, e che a buon diritto fu impiccato (accusa [3]). XIV. Asserire che anche i profeti e gli apostoli furono maghi e che quasi tutti vennero a mala fine (accusa [15])4.

Running this through the ever more amazing Google Translate:

I. Denying transubstantiation (charge [4]). II. Questioning the virginity of Mary (charge [8]). III. Have resided in countries experiencing their way of heretics (charge [10]). IV. He wrote against the Pope of the Beast trionfante2 Outlet. V. Support the existence of innumerable worlds and eternal (charge [5]). VI. Claiming metempsychosis and the possibility that tell one soul two bodies (charge [6]). VII. Feel the magic of good and lawful (charge [7]). VIII. Identify the Holy Spirit with the soul of the world (the complaint). IX. To say that Moses and his miracles invented simulates the Law (charge [14]). X. Declaring that the S. Scripture is not a sogno3. XI. Believe that even the demons will be saved (charge [12]). XII. Preadamites opine the existence of (the complaint). XIII. Claiming that Christ is not God, but deceiver and magician, and that rightly was hanged (charge [3]). XIV. Claiming that the prophets and the apostles were magicians, and almost all were in bad order (charge [15]) 4.

From which we extract:

V. Support the existence of innumerable worlds and eternal (charge [5]).

I also found a Vatican reference (notice the "va" domain), which mentions:

In one of the last interrogations before the execution of the sentence... the Dominican friar was questioned by the judges of the Holy Office on his cosmogony conception... Even then, he defended his theories as scientifically founded and by no means against the Holy Scriptures... (Circa motum terrae, f. 287, sic dicit: Firstly, I say that the theories on the movement of the earth and on the immobility of the firmament or sky are by me produced on a reasoned and sure basis, which doesn’t undermine the authority of the Holy Sciptures […]. With regard to the sun, I say that it doesn’t rise or set, nor do we see it rise or set, because, if the earth rotates on his axis, what do we mean by rising and setting[…]).

This is indirect evidence, but it is evidence. Why at this late stage is Bruno defending these theories as scientifically founded and not against the Holy Scriptures if he is not on trial for these theories (among others)? Of course, being on trial for these theories is not the same thing as being convicted for these theories - so I say, it is only evidence, not proof, of the reason for conviction. (Though, that he was put on trial for these theories - which I think is much more well established by the evidence than that he was convicted for them - is itself bad enough.)

[edit - the phrase "before the execution of the sentence" suggests that the statements are made after conviction; it is not clear to me how this alters its import as evidence, though I tend to think it strengthens it, because he is saying these things in light of his conviction]