Hello & welcome to net54,
It's not possible to nail down anything based on the 44 on the front of the ticket. IMHO, 44 would refer to the 44th home game, but I may be wrong.
One question about the date written on the back of the ticket:
Is the writing in fountain pen, or is it in ball point pen?
I can't tell by your photo.
Please note that ball point pen was not a thing until around 1940. If the writing is in ballpoint pen, it's inconsistent with 1934.
BTW, my good friend Dan Busby (RIP) published a couple of limited production books on ticket collecting entitled "Washington Senators 1868-1939" and Washington Senators 1940-2012", respectively.
Unfortunately, there is not an example of a photo of a Grandstand ticket from the 1934 era to compare it to in the book. The ticket price is consistent with what a Grandstand ticket cost in the early 1940's (1941) based on an exemplar that he shows in the 2nd book.
I hope you find this helpful.
