Yes, as someone stated before me, the easiest way to do this is to use the notify button. It is located on the top of this thread window. By enabling email notifications, you will get notified every time a new bounty thread is created in the bounty subsection of this forum. But beware, when you get new mail, it says "More topics may be posted, but you won't receive more email notifications until you return to the board and read some of them.", so you will have to actually open threads provided with a link in the email to keep getting notified. There is also another way, but is much more tedious. You can simply navigate the bounty subsection and click on bounty threads that have a small amount of views/replies - those ones are probably brand new. I usually do that for the first 10 pages, because I reckon that if the thread is not there after some time (few days maybe), then it is not worth checking out.
Where notify button?
Hey there, the "Notify" button is right there on the top of your first post on the far right side, where there are several other buttons (Reply | Unwatch | Notify | Mark unread | Print). Now, I also use "Watch" button from time to time, which puts the thread under your "Watchlist". You can access that section following this link: https://bitcointalk.org/index.php?action=watchlist
If you need more help, just ask or send me a PM.