How should I have continued after move 30?

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Billymill

Question:  how should I have continued after move 29?
This was at a simul event with a GM playing about 20 opponents.  He killed me off quickly & easily but then, very sportingly, invited me to reset the pieces for a second game.  This is that second game.

I am an inexperienced, lowly-graded player (just gained Yorkshire CA rating 78), was initally intent just on surviving as long as possible against a GM but then threw caution to the winds and attacked.  To my absolute delight I won a bishop from him as a by-product of attacking his king.  Arguably I had the stronger position at that point (move 29).

I think a better player than me should have won from that position.  Alas, I wasn't up to the job and things went downhill quickly as soon as the GM started giving serious attention to the matter.  (And I made some pretty stupid moves, too.)

So my question is:  what should my tactics have been after taking his bishop at move 29?  Could I have won if I had just played sensibly?

Billymill

Thanks, pals, for those very helpful comments & ideas.  All much appreciated.  Particular thanks to Gambitking for taking the trouble to set out an alternative line of play after move 29.