I tried to read some threads and google search, but most of what I find is either too old and the pictures are removed, or it's stuff for drops.

Is this the right direction for me to wrap bullhorns?

yes

Thats how I wrap mine. It should tighten the tape as you ride.

not sure if it matters, but my bars have no drop.

Hey what do you know that's exactly what I do these days. But I don't remember choosing to do this way. See? Never crossed my mind. I was like ... Wrap it right? Dah. May be I should pay more attention?

On any kind of bar it's good to always tighten the tape in the same direction your hands naturally rotate. This creates a wrap that tends to be tightened rather than loosened by your hands' natural motion. On bullhorns and bar tops, your hands rotate across the top and towards the outside, so wrap em that way.

Whatever works though, if your wrap is nice and tight it probably won't come loose either way. Just try not to have both sides going the same direction, cuz it looks incorrect: i.e.

not like this:

\ ..... \
\ .....\
\ .....\

or this:

/....../
/....../
/....../

but like this:

\ ..... /
\ ...../
\ ...../

or this:

/......\
/......\
/......\

Alright thanks everyone. That's what I thought I had been reading, but I'm more of a visual learner and wanted to confirm before I started wrapping. I bought some cheap bar tape to try things out with since this will be my first wrap job.

Just go carefully, checking esp. on the outside of bends that you have enough overlap so that no bar is showing; and try to pull your tape just about as tight as you can without breaking it (this is the #1 way to prevent premature unwrapping). since you're wrapping bullhorns you will have tons of spare tape for do-overs should anything go wrong.

Just remember to have the tape on the outer side of the bar, the side that faces you and wrap the tape back to you. As mander stated, stretch it tight and you could always redo it if you messed up, it's not the end of the world

Run them bare

?

Nonononononononono!

that's how I wrap any bar

I thought about it, but I figured I'd get ridiculed on the forum.

I also considered track grips, but the tape I bought was $5... so if I want to try something new it won't be like I'm losing much.

Bare is fine, but only if you wear grippy gloves (like baseball batting gloves, $20). But, otherwise, bar bars suck because when your palms get the slightest bit of sweat your hands will slide around a lot. Not a good idea at all.