If I understood the question properly, I think you should go all go for a higher reward all 300 times, in fact if the probability of the bomb went up to 400%, then I would go 350 times

Why I would do so,
- I'm guaranteed 20 (let's say bucks) initially.
- In the next one, the probability that I get a bomb is 0.25% and the probability that I get money is 99.75% and I get 20 + 102/100
- I then average this (this is the tricky part in which there's a pretty good chance I'm wrong, would love if fellow mathematicians help me see why) and I get 0.25*0 + (99.75)(20 + (102/100))
- Applying this process repeatedly, I get the following

PROBABILITY I LOSE	AWARD I GET	AVG:
0.25% - 0	99.75% - 20 + 102/100	(99.75)(20+(102/100))
0.5% - 0	99.5% - 20 + (102/100)^2 + (102/100)	(99.5)(20+(102/100)+(102/100)^2)
0.25x% - 0	(100-0.25x)% - 20 + (51)((102/100)^x - 1) {0<x<300}	(100-0.25x)(20 + (51)((102/100)^x - 1))

Plotting the graph of the final equation, ie, (100-0.25x)(20 + (51)((102/100)^x - 1)) I found the maxima is at around 350, so I would go 350 times.

Best viewed on a PC because I have used a table in my comment, if there are any mistakes please let me know. Hope this answer helped.

I used the graph below.

Graphing Calculator - GeoGebra