I offered a draw against my highly rated opponent (current club champion), which was accepted after two minutes thought. I can't help thinking that I may have had more. Opinions please. 

White looks lost

What if white plays 2 Rd4, with the intention of chasing the black bishop up and down the a5-c3 diagonal?

I would have played on as Black.

You could have tried, but mosst likely it would have been a draw.

I think you are correct, if black presses, he might lose. Draw out of fear, nice move 

I think the position's drawn with best play, but it's not so simple.

fotoman, in your variation 3.Bb3 is the move that causes White to lose.

 

That game looks good for white to me, and I agree with likesforests, Bb3 was a bad move to play, Ra7 or 8 was stronger.

Am3692 wrote: That game looks good for white to me

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It should be noted that black has the draw in the bag. The white bishop must stay on the d1-a4 diagonal, so black can chase the bishop endlessly with his rook (along the 8th rank). This tactic will lead to a draw either by agreement or repetition in a few moves.

You definitely do have a draw. You can chase the white bishop until repetition. However, I don't see how you have more. 1...a4 loses to 2.Rd4 as you said. Where did you think you had the resources for a win?

There are some complications:

1 Bc2   a4    2 Rd4   a3  3 Rxb4 Rc1

If White plays 2.Rd4, Black can force a win. The original position is drawn.

 

1. Bc2 a4 2. Rd4 a3 3. Rxb4 Rc1 4. Bb3 Rb1 5. Rb5 a2 6. Rf5+ Ke7 7. Re5+ Kf6
8. Re6+ Kg7 9. Bxa2 Rb2 10. Re2 Rxa2  -+.

Yes, I've seen a few positions now K+R Vs K+3P and K+Q Vs K+R+3P, but all are tough finishes, not forced wins.

 

At the time I was thankful to get away from the table, my opponent had outplayed me in the opening and middle-game, making a mistake at the first time control.

What about this? Pretty lines.

in above line if 6Rxa2 then Rxc2, 7Ra1 then Rf1

Fotoman, there's a flaw in that plan. What if, 6.Ra7+?

 

Black's king is very confined. He can't step on the a2-g8 diagonal due to Bc3+, he can't step on the a1-h8 diagonal due to h7, he can't step on the c-file due to Rxa2. That really only leaves a small corridor... d6, d7, d8, e7, e8, and f8. So White's rook can get away with perpetual checks from a6, a7, and a8... draw.

 

tricky endgame situation, I love it!

I wasn't sure about 2. Rd4 but 2. Ra7 looks even worse 

White can prevent the rook trade by playing 6.Kh1 in the variation but it doesn't help much. 

 

 

 

The Rook vs 3 Pawns finish in the 2.Rd4 line: