Bishop's opening =Roy Lopez Reversed?

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.

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.

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

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.