Did the Blessed Virgin shed blood during the Nativity?

What!?

No, no, no!

She is a Virgin whose spotless purity remained integral before, during and after childbirth and yet remains forever intact. Therefore, no physiological effect was had adversely upon the Immaculate Virgin's body, according to the many types and oracles in the Old Testament as shown above. In the Roman Breviary there is a Responsory (Feria IV infra Hebdomadam I Adventus) that says:

Ante multum tempus prophetavit Ezechiel: Vidi portam clausam; ecce Deus ante sǽcula ex ea procedebat pro salute mundi: * Et erat iterum clausa, demonstrans Virginem, quia post partum permansit virgo.
   V. Porta quam vidisti, Dominus solus transibit per illam. * Et erat iterum clausa, demonstrans Virginem, quia post partum permansit virgo.

   
This alludes expressly to the Prophecy of Ezechiel, cap. xliv. 2.

The inviolate virginity of Our Lady during the Nativity of her Divine Son is de fide.

What's the best church docuмent to read that explains the Perpetual Virginity?

I don't have the Denzinger with me at the moment, but three magisterial docuмents I remember that clearly state the perpetual virginity of the Mother of God are:

1) The third Canon of the Lateran Synod (649)

2) The Apostolic Constitution cuм præexcelsa (27 February 1477) of Pope Sixtus IV

3) The Apostolic Constitution cuм quorumdam hominum (7 August 1555) of Pope Paul IV

The Bulls Munificentissimus Deus (1 November 1950) and Ineffabilis Deus (8 December 1854), wherein Popes Pius XII and Pius IX define the dogmas of the corporeal Assumption and Immaculate Conception of the Blessed Virgin Mary, respectively, ought also to be consulted.

St. Alphonsus and St. Louis-Marie give the best expositions of Our Lady's virginal Maternity, both as regarding Our Lord Himself and her spiritual maternity of the Church to whom she was entrusted by her Crucified Son, "Mulier, ecce filius tuus" (Joann. cap. xix. 26); for the which reason the Blessed Virgin was with the Apostolic College to receive the Holy Ghost, even though she is the Immaculate Conception, having been the predilect dwelling of the Holy Ghost since the first moment of her existence, "Hi omnes [i.e., Apostoli] erat perseverantes unanimiter in oratione cuм mulieribus, et Maria matre Jesu[/i]" (Act. cap. i. 14).