Thanks to Chess.com's live chess, I have been practicing my main opening for white, the bishops opening and vienna game. Often, I encountered 1. e4 e5 2. Bc4 Nf6 3. Nc3 Bb4!?. I went on Wikipedia and wikipedia gives the roy lopez line: 1. e4 e5 2. Nf3 Nc6 3. Bb5 Bc5 4.c3 Nf6. 

Perhaps in my games I should play 4. Nf3!? leading to Kings gambit declined by transposition, or a Gambit if black plays ...Nxe4?!

Feel free to post comments on what you think is the right move in the position. Usually I play 4. Nge2 or d3.

Simply 3.d3 is probably best. After 3.Nc3, you occasionally get these pests who play 3...Nxe4. Or you can mix it up with 3.Qe2!?, which wins in all variations.....

You left out Rob Roy....... No, not Liam Neeson...... one of these. Think I'll have one right now.......

2...Nxe4 Challenge excepted! 3. Qh5!! and white mates in 438. Actually, I have never played against Nxe4 on this website. I doubt many begginers even know about that move. Almost everyone plays the moves I discussed formerly, namely 2...Nc6 or 2...Bb4.

It's better than the usual Bishops opening. (Nc3 instead of d3). White plays 4.Nge2 and black doesnt have his usual responsce, d7-d5. Also if he tries Nxe4 (Nxe4 d5) white has a free tempo with c3 attacking the bishop.

So white would like to play Nge2 - 0-0 - d3 and f4 here with a good game. Black could play c6 and d5.

After 4.Qh5, black gets some advantage after 4...Nd6 5.Qxe5+ Qe7. But you're right, many players don't know the line. After 3...Bb4 4.Nge2, black can still play 4...Nxe4. In fact it might work better then. It's not clear that white gains a tempo with c3: 5.Nxe4 d5 6.c3 Be7 7.Bd3 (7.Bb3 may be better) dxe4 8.Bxe4 f5!?

That's why after 4 Qh5 Nd6 white plays 5 Bb3! which leads to enormous complications.

You may be right about 4 Nge2?! Nxe4! it doesnt seem to give white much...

So 4 d2d3 leads to a proper bishops opening, 4.Nf3 transposes to more common theory

a3 is Ok. 5...Nxe4 is a lemon, though. Black can just castle or play 5...d6. Even 5...h6 is probably alright. After 4.a3 Bxc3 5.dxc3 d6 white usually continues 6.Nf3 or 6.Bg5. I was looking at this line with a friend. In a blitz game I tried 6.f4!? Nxe4 7.Bxf7+ Kxf7 8.Qd5+ Be6 9.Qxe4 Nc6.10.f5!?

Playable for certain, but black is unlikely to play Nxe4?, which is bad because exchanging the e pawns favours white (black will not archieve a kingside majority if he exchange the e pawns, and that is supposed to be his compensation for the missing bishop pair in those structures). As black i would play something like 5...O-O 6.Nf3 Re8 and then playing for d5, probably with c6 in some lines.

Yes, 4.Qh5 is complicated only if black wants it complicated. 

Right, I know that Nxe4 is dumb, was just playing it out for demonstration.  The way I see this entire situation: Black is stubbornly trying to play out Ruy Lopez, but doesn't grasp the tempo advantage is needed to complete the line.  At some point, your white B is going to be in just the right place to thwart his plans.  Here's what happens if you just play along:

False. it's clear that his opening falls apart if you make him blunder a pawn, but what about c6 before d5? it turns out that the Bc4 is not so well placed at all. And if it moves again, white is a tempo down and not a tempo up on normal exchange lines.