As mentioned, bumpfee won't let you do this, but if you do attempt it with a raw transaction, note that you will have to bump the fee relative to the entire package of transactions. So if you are bumping the fee of a transaction with a lot of descendants, you will need to calculate the total package size in bytes, then bump the fee accordingly.
Are you thinking of CPFP (Child-Pays-For-Parent)? 
If so, that works the other way... when you're trying to get one of the descendants confirmed quickly, you have to take into account all of the ascendants.ie. if you have the following chain of transactions: TransA -> TransB -> TransC -> TransD -> TransE
And you bumpfee on TransA... then B, C, D and E will become invalid as the hash of TransA will change, making B invalid.
If you're wanting to get TransE confirmed quickly, then you would need to take A, B, C & D into account as well, to make sure that the fees are big enough for miners to want to get all 5 transactions included in a block.
Are you familiar with RBF pinning? This is a good explanation of the issue I have described. CPFP is subject to the same principle. If I could just kick out transactions w/ descendants from the mempool without paying for the full package that would be a DoS attack of sorts. Unfortunately it can also be turned on its head to "stick" transactions.
https://bitcoinops.org/en/topics/transaction-pinning/
