1.) e4-c5

2.) Nf3-e6

3.)Bc4....

If your white then Bc4 is probably not the best move. With black already have moved e6, then Bc4 is just a move that clears the way for the king to castle.

I've heard Bobby Fischer played it.

But c4 isn't necissarily the best square for the bishop.

3.Bb5+ is the Rossolimo attack and is abetter alternative.

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 They played e6 not d6 so the Bb5 lines aren't available. They just play a6 and gain time.

It would be sound if black had played d6 first, but here it is slightly dubious.

The problem is white is going to (Eventually) play a d5 thrust, gaining space in the center with tempo pushing the bishop.  So its slightly dubious.  Playable sure, but why play something worse then you need to?

Bc4 in the sicilian is a common theme.   It is normally played later than move 3 when it has a greater impact, e.g. see the Sozin lines.  That being said it is normally of less useful in the e6 Sicilians.  It appears that Black, by playing e6, has taken you away from your comfort zone/pet anti-sicilians.  You need to recognize that and either prep a line for the e6 or switch to a different start, perhaps 2. Nc3, c3, Ne2, d4, f4 etc.

BTW 3. Bc4 in the sicilian is a common thread in the forums.  Trying finding some old threads for further ideas.

it's strange because my computer always plays that line against me in long games, and a pawn push always results in my loss...

Superficially it has sting and rushing d5 plays into it.  Everyone thinks the Sicilian is all tactics but it is not.  There are important strategic and positional themes as well.