The problem is an old one its due to extra biomes replacing vanilla biomes, this means that if extra biomes adds 10 more biome types in over writes 10 vanilla biomes this then means that you are 10 times less likely to find the one you want, the numbers are just for show I have not counted the extra biomes but a guess would be 10+, & we all have been in that position of looking for cacti for water proofing pipes, if you are using DW or a pack with ee, use the minium stone to convert flowers etc.
if not just keep hunting you will find in the end.
Not quite. The extra biomes types don't replace any vanilla types. Both are sort of added to a list. When the random generation occurs, it thinks: ok, I need to create this new chunk. Step 1, what biome(s) should it be? It then looks through the list and picks.
The problem is that the more biomes you have, the odds of getting any 1 decrease. So, if there were 10 biomes ( assuming an even odds for each biome ), then a random chunk would have a 1 in 10 chance of being that biome. If there's 50, it's a 1 in 50 chance...which is getting to be pretty poor odds.
This is compounded by the fact that it isn't a simple per chunk choice. Biomes usually aren't a single chunk in size. Instead, they are quite large. If the average biome was something like 200 chunks, and there were 50 biomes, that would give you an area of 10,000 chunks to have 1 of each biome. So, on average you would be looking at an area of 100x100 chunks to find just 1 instance of your given biome. That's 1.6KM x 1.6KM. Add in having a little bit of bad luck, and you could easily be looking at substantially more than that. In fact, even if you ran straight for 114 new biomes, there's still a nearly 10% chance you would not have hit a given biome.
Note: All of these numbers are random ones picked to show my example. They are not the actual numbers.
Something I can do to help though: Don't run through the middle of biomes. Biome lines often meet up, so follow the lines.
PS: On the size of the map. It's something like 1/8 the size of the surface of the Earth. Yea, it really is gigantic. You could fly for weeks before you would hit the edge. Even in the nether we are talking a large amount of time to get there.
FYI: A block is 1m by 1m. ( just over 3 ft x 3ft )