Republicans haven't been about fiscal conservation in a while.
It's also a mistake to just look at who controls the White House to figure out which party is in control when the economy does well economically. Both the executive and legislative branches matter and for the legislative, you need to control both houses. Even if one party controls the excutive and both houses of congress, it's hard to attribute the success of the economy to the current controlling party. Somethings the economy might be doing better because of current policies and sometimes it might be doing better because of policies enacted by the previous administration and congress, but the effects were latent.
In general, you can't take a macro look to determine which party is better for business. Instead you've got to look at things on a policy by policy basis and look at the first and second order economic impacts of specific policies.
Also, while Republicans haven't been very fiscally conservative in many years, most of the "huge bills being run up" are only sometimes from new spending. Most of the time, running up the bills is just from tax cuts. The democrats pass spending bills with accompanying taxes and the republicans are unable to undo both the spending and the taxes at the same time, so they negotiate for at least cutting taxes to help the economy, but the spending gets left in place.
The truth is that both parties are generally drunken spenders, but that one party has no issue taking more money from productive Americans to pay for their drunken spending.
FWIW, I'm neither a republican nor a democrat. Both parties are awful, but at least the Republicans try to let people keep money they've earned and rarely try to raise new taxes.