Hard inquiries are not, in and of themselves, bad things except under certain circumstances.
For instance, if there is a sudden flurry of new hard inquiries on your credit report then it is a good indication that you're shopping for credit, and that could be a red flag that causes potential creditors to decline you.
A hard inquiry that has a corresponding new account opened as a result is not a negative, because clearly the creditor who ran the inquiry found you to be creditworthy.
Higher credit scores come from a couple of different factors. First, the age of your credit accounts plays a large role in determining the score. The mix of credit types (credit or revolving charge accounts, installment loans such as auto payments or mortgages, etc) is another consideration. Payment history obviously matters.
The big "no no" (and it sounds like you've avoided it, unlike most consumers) is having high balances on your credit accounts. Ideally with credit cards, you don't want your balance to run more than 15% or so of the available limit. Any higher than that and it could (to a creditor) be an indicator that either you are not good at managing credit or you are using credit cards to live beyond your means. Either of these is negative.
Having one credit account is not terribly helpful, and the threshold (according to Equifax and TransUnion) is around 4-5 credit accounts of varying types in order for their scoring model (Vantage 3.0) to develop a really good picture of how well you manage money and credit.
Interestingly, CreditKarma has a feature on their site that lets you simulate how your credit score might be affected by adding new credit. It will show, based on your history, what your score would change to depending on the type and size of a new credit account, and it's well worth trying out. CreditKarma's free, and so is the use of the credit simulator tool, so it may be worth looking into for a better answer to your question.