Hey there! You asked about Big Bend... The FIRST thing you'll need to decide is what time of year you'd like to visit. Temps can get hot, but sometimes that is the draw. More heat = less people. You can sometimes be one of a handful of people in the entire place without subjecting yourself to Death Valley temps.
The second thing is to decide how much off trail walking you will do. A lot? A little? Your gear list will change depending on this answer. I can't really advise you of what to do yet without having more info about what you LIKE to do. Hike? Take pics of stars/night scenery? See ruins? Watch wildlife?
The third thing is to over prep for the place. It is rugged... More than most places you can imagine (unless you've lived on a ranch or some other rugged environment for an extended period of time). Mostly this is just to ensure that you have a backup in the event of something going wrong. As long as you stick to the plan/trail/etc, like any other wilderness outing, you should be fine having only walked away with some cool pictures and a new insight.
There are bears, but they are Texas (Mexican) Black Bears. Timid, mostly eat roots and berries... Always run from people when discovered... There are mountain lions, and those can be their own experience, but that depends on how one carries themselves. And there is of course the desert heat if you spend your time down in the desert vs. up in the mountains.
Let me know more about what you want to do and I'll give you more insight. Drop me a line "offline" to get a quicker response. stingrey@ stingrey.com. Hope to hear from you soon!
Rey