From the Victoria History of Yorkshire Vol. III P.146 -

The seal of Abbot John de Birdsall (1304-13) is a small vessica (=vesica? - blister shape?) 1 1/4" by 3/4" with a design of a naked arm, the hand holding a crozier, between two suns and as many moons. (Cat. of seals B.M. 3367 Add. Chart. 16688)

From the Coucher Book of Kirkstall Abbey
Brother J. de Bridesal was proxy for the Abbot in proceedings respecting a contract for the sale of the Abbey's wool to The Society of the Betti (merchants of Lucca).

YAJ Rec.Vol.17p110
John de Brydesal of Kirkestal is bailiff to the Abbott of Kyrkestal in a complaint. A.D.1291. He subsequently became Abbott himself in A.D.1304.

From the Victoria History of Yorkshire Vol. III
P.145 - John de Birdsall Abbot of Kirkstall 1304-11 elected1304 (York Archiepis. Reg. Corbridge fol.21). occurs 1311 (Add. Chart. 16782).
NB the next Abbot (Walter) was elected 1313 (York Archiepis.Reg. Greenfield, slip between fol.77&78)

Surtees Soc. (1937)
Archbishop Greenfield's Register Vol.4
"1909 18kal.Feb (Jan.15,1310-11) at Cawode (Cawood).
"John de Briddesale appointed Abbot of Kirkstall".????
IT IS CLEAR FROM OTHER SOURCES THAT JOHN WAS ABBOT FROM 1304.

From Surtees Soc. Vol.cxiii (1906)
Records of the Northern Convention of the Trial of the Templars - 1310. - Amongst those cited to the "Provinciale Consilium" was J. Bridesal, Abbot of Kirkstable (Kirkstall).
From Thoresby Soc. Vol.1 - The Abbot of Kirkstall Abbey 1304-1313 was John de Bridesall.

From Thoresby Society Vol. 58 p. 48
A number of abbots (of Kirkstall) were members of local families. Hugh de Grimston and John de Bridesale who had both been monks of Kirkstall before becoming abbots were almost certainly connected with local families of some importance and linked by marriage (Coucher Book pp. 137-8). The de Bridesale or Birdsall family had been lords of the Manor of Clifford at least since 1166 and were benefactors of the Abbey. John  de Bridesale accompanied Hugh de Grimston on his journey to Edward I in Gascony in 1287. During John's abbacy in 1313 a William de Bridesale granted land in Bramley to the Abbey having obtained leave to alienate a mortmain.

From the MS. Chronicle of Kirkstall

"To his reverend brethren the prior and convent of the Monastery of Kirkstall, John, styled Abbot of the same wishes health and grace, and that they may labour more earnestly after the things which concern religion, peace and charity.
Beloved, we have written this letter in haste from Canterbury, knowing that an account of the success of our journey will be pleasing to you.
In the first place, our dear brother, who was present, will inform you that on the morrow of St. Laurence we were met by letters from the king, in a very threatening style; that we were apprised of robbers who laid wait for us in the woods under a rock ; and that we were bound, under the penalty of forfeiting all our goods, to abide the king's pleasure. However  having been at length dismissed from his presence with honour, we proceeded on our way ; and, notwithstanding a delay in London, arrived at Canterbury on Monday evening, ourselves, our servants, and horses being all well. We were not without hope, therefore, that our feeble beginnings will be followed by better fortune. On Wednesday morning, the wind blowing fair, we put the horses on board a ship ......
For the time to come we commend you, dear brethren, to GOD, and our bodily safety to your prayers.  But especially pray for the salvation of our soul; for we are not greatly solicitous if this earthy part of us be delivered into the hand of the wicked one, so that the spirit be saved in the day of the Lord, which we hope for through your intercessions ; we should wish, if it be the will of GOD, to be committed to the earth by your hands, wherever you shall dispose.
But know assuredly that, if we return, whosoever appears to have been most humble in conversation and active in business during our absence shall receive an ample measure of grace and recompence from God, and shall every ... be more affectionately regarded by us.
We entreat and enjoin brother R. Eckisley to prepare himself for the duty of preaching on the Nativity of our Lord, unless we return in the meantime, that so great a festival may not pass without a sermon, a thing which hath never yet happened, nor, by the grace of GOD, ever shall do.
We wrote unto certain persons, 'abstain from every appearance of evil, and avoid it beforehand, whatever is or may be pretended in its behalf.'
GOD shall give you the knowledge of these things.
We adjure you, brethren, by the bowels of mercy in Jesus Christ, that, if ye hear of our departure, ye will pray for us faithfully, remembering the labours and distresses which we endured in the beginning of our creation, and of which ye are now reaping the fruits in peace.
Ye know, dearly beloved, that worldly occupations, such as we have long been entangled in for your sakes, are not without        danger to the soul. But we derive great -hopes from your compassion, seeing that we aim at no earthly advantage, nor consume the revenues of the monastery without cause.
      Salute our dear friends :...................
     especially our dearest companion,* to whom we would have some one interpret this letter.  When he hears it he will scarcely be able to refrain from tears, which he shed abundantly at our parting. We commend our poor mother to your compassion. - Salute one another with an holy kiss.
The salutation of me, John, your minister, such as I am, and studying to do everything in my power for your advantage and honour. We commend you again and again to God and the B. V.
Written at Canterbury, with many tears"
The above was sent fom Dover while the Abbot was on a journey to the Continent partly on the King's business, but also perhaps on his way to the General Chapter. (This may have been in 1312 when the Abbot was granted royal protection perhaps to attend the General Chapter).