Can beams be up against a post base like this

The Scout Pioneering website contains information on how to build several bridges. I am guessing that most of these are more complicated than what you had in mind, so if you want something simpler, you can attempt flat span bridge using 2x12's for a span between 14 and 18 feet. On the latter page the author goes on to say that "[i]f you are thinking of building any bridge with a span greater than 20 feet, you better get a structural engineer involved, plain and simple", which I am inclined to agree with.

Note that none of those links say anything about the actual load-bearing capacity of the bridges, but I would assume that most of them would work fine for one or a few people crossing at a time.

If you want to calculate maximum load, it is complicated, especially as the materials in the bridge are likely to deterioriate over time - especially if the environment is wet. Some simple calculators for point loads and distributed loads can be found online to give you an idea of what your bridge can take, but as they make clear on their website, they provide no guarantees. In other words, if you want someone to guarantee you that your bridge is safe, you'll most likely have to hire an engineer, as circumstances change from bridge to bridge.

There are lots of ways to attach beams to posts, and you don't necessarily need purpose-built brackets. Miter your beams so that they come together at an appropriate bisection of the post top, and use whatever means is convenient to keep them positioned... dowels, angled screws, etc.

In the case shown in the second image, I'd be inclined to use a skewed hanger and hang the angled beam on the other two. If your beams actually have the offset shown, things are complicated a bit, but maybe a short third member bolted to the right-hand beam would flush things up in simple fashion.