Slow MySQL InnoDB performance of table with 100 million rows
Are there multiple rows for each dna_bits?  If not, then that column could be the PRIMARY KEY?  If you can do that, then the speed might double because you won't be bouncing between the secondary index and the PK.  Getting rid of p_id and the secondary key would save space.

How much RAM?  How big is the table?  (I would guess 5GB data+index.)  What is the value of innodb_buffer_pool_size?  If that can be set to 70% of available RAM and still be bigger than the table size, then (eventually) all the data you need will be cached.  Again a speedup.  (Can't tell how much.)  This is because of avoiding I/O.

10K lookups will take some time.