Well I have been doing test on the heat bed recently mainly testing every bed for the next batch of printers but also any RMAs we get in trying to find out why they failed,stop working,blow fuses. Originally I was just testing or rather looking at each bed with a thermal camera to see there was any thing wrong thermally. Usually test on a bed would only last about 15 mins or so. However after over a 150 heat beds I had blown at least 2 fuses, 2 melted connectors, and had wire that had melted threw its insulation and shorted out blowing out another fuse I started to look at what the power each bed was pulling.
Sadly it looks like a good heat bed has a resistance of 0.65 ohms at room temp, and around 0.8 when at 85C. That means as the bed heats up it pulls more than 15A for at least a minute every time you turn it on. Which is not necessarily bad but not great either. I have recently found out that fuses don’t immediately blow right after the current goes over their rating, how far the current goes over the rating determines how long it will take. For example the fuse we ship with the TAZ (http://www.littelfuse.com/data/en/Data_Sheets/Littelfuse_Fuse_287-ATOF-CN.pdf) for current at 110% the rated current(16.5A) it can take at least 100 hours for the fuse to blow. At 135%(20.25A) it can take as long as 10 minutes for the fuse to blow. For the TAZ since the high current last only a little while on a good bed it can take as many as 10,000 cycles of heating up the bed up from room temperature for the fuse to blow. For beds that have a resistance of less than than 0.65 ohms at room temp they can pull a decent amount of current. One bed I tested was only 0.56ohms and pulled as much as 18.5A at room temperature. It managed to melt the connector on the test Rambo I was using before the fuse blew and before I could turn off the power.
So switching to a higher rated fuse would mean that the fuse might not blow, but the next weakest link in the system which could be anything from the Rambo connectors to the wire to the heat bed or even the quick connects attached to the switch.
The only decent solution I have come up, besides trying to use a huge bulkly 200W resistor in series with the bed, is to use PID control for the heat bed. For the default firmware with that shipped with the TAZ we just used bang bang control, basily on-off. Using the PID in the firmware we can in sense limit the voltage to the bed, and indirectly limit the current the bed pulls. The hard part for me has been deciding/testing how much to try limit the current so that all heat beds, good, bad and weird would still be able to at least reach 85C in a reasonable amount of time, yet as low as possible so to try and get the current as far under 15A as possible. I will try and post a link, probably tomorrow, to the firmware I have have been testing so you can look at it. Right now I think have the pwm limit set to 242 out of 255, kp=650, ki= 60 and kd=1850. Since you would be doing this for a single machine you could very easily try something lower. Without knowing the resistance of you bed, but based on how long it takes a fuse to blow you could try something around 220 and see if you can still reach 85C.
TL;DR No on bigger fuse, firmware can help, and sorry for the wall of text.